simulation of simultaneous events in regular expressions

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University of Pennsylvania University of Pennsylvania ScholarlyCommons ScholarlyCommons Departmental Papers (CIS) Department of Computer & Information Science April 2004 Simulation of Simultaneous Events in Regular Expressions for Simulation of Simultaneous Events in Regular Expressions for Run-Time Verification Run-Time Verification Usa Sammapun University of Pennsylvania Arvind Easwaran University of Pennsylvania Insup Lee University of Pennsylvania, [email protected] Oleg Sokolsky University of Pennsylvania, [email protected] Follow this and additional works at: https://repository.upenn.edu/cis_papers Recommended Citation Recommended Citation Usa Sammapun, Arvind Easwaran, Insup Lee, and Oleg Sokolsky, "Simulation of Simultaneous Events in Regular Expressions for Run-Time Verification", . April 2004. Postprint version. Published in Electronic Notes in Theoretical Computer Science, Volume 113, 3 January 2005, pages 123-143, Proceedings of the Fourth Workshop on Runtime Verification (RV 2004). Publisher URL: http://dx.doi.org/10.1016/j.entcs.2004.01.030 This paper is posted at ScholarlyCommons. https://repository.upenn.edu/cis_papers/89 For more information, please contact [email protected].

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Page 1: Simulation of Simultaneous Events in Regular Expressions

University of Pennsylvania University of Pennsylvania

ScholarlyCommons ScholarlyCommons

Departmental Papers (CIS) Department of Computer & Information Science

April 2004

Simulation of Simultaneous Events in Regular Expressions for Simulation of Simultaneous Events in Regular Expressions for

Run-Time Verification Run-Time Verification

Usa Sammapun University of Pennsylvania

Arvind Easwaran University of Pennsylvania

Insup Lee University of Pennsylvania, [email protected]

Oleg Sokolsky University of Pennsylvania, [email protected]

Follow this and additional works at: https://repository.upenn.edu/cis_papers

Recommended Citation Recommended Citation Usa Sammapun, Arvind Easwaran, Insup Lee, and Oleg Sokolsky, "Simulation of Simultaneous Events in Regular Expressions for Run-Time Verification", . April 2004.

Postprint version. Published in Electronic Notes in Theoretical Computer Science, Volume 113, 3 January 2005, pages 123-143, Proceedings of the Fourth Workshop on Runtime Verification (RV 2004). Publisher URL: http://dx.doi.org/10.1016/j.entcs.2004.01.030

This paper is posted at ScholarlyCommons. https://repository.upenn.edu/cis_papers/89 For more information, please contact [email protected].

Page 2: Simulation of Simultaneous Events in Regular Expressions

Simulation of Simultaneous Events in Regular Expressions for Run-Time Simulation of Simultaneous Events in Regular Expressions for Run-Time Verification Verification

Abstract Abstract When specifying system requirements, we want a language that can express the requirements in the simplest and most intuitive form. Although the MaC system provides an expressive language, called MEDL, it is generally awkward to express certain features like temporal ordering of complex events, timing constraints, and frequencies of events which are inherent in safety properties. MEDL-RE extends the MEDL language to include regular expressions to easily specify timing dependencies and timing constraints. Due to simultaneous events generated by the MaC system, monitoring regular expressions by simulating DFAs would result in a potential problem. The DFA simulations would involve concurrent multi-path simulations and result in exponential running time. To handle simultaneous events inexpensively, we generate a dependency graph to identify possible simultaneous events. Further, we augment the original DFAs with alternative transitions, which will substitute for multi-path simulations.

Keywords Keywords Run-time verification, regular expressions, temporal logic, dependency graph

Comments Comments Postprint version. Published in Electronic Notes in Theoretical Computer Science, Volume 113, 3 January 2005, pages 123-143, Proceedings of the Fourth Workshop on Runtime Verification (RV 2004). Publisher URL: http://dx.doi.org/10.1016/j.entcs.2004.01.030

This conference paper is available at ScholarlyCommons: https://repository.upenn.edu/cis_papers/89

Page 3: Simulation of Simultaneous Events in Regular Expressions

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Page 4: Simulation of Simultaneous Events in Regular Expressions

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V ? � ' A ' � � � � ' � 4 � ' ? $ � > > � $ � � � � I & 4 � " � ' � 4 ? C � � � � � � � � � � � ? 4 - � � & 4 � - 4 ? � 8Y + 4 � - 4 + � i � � � D � � � � < � $ + � � � � I � � � & 4 � " � ) � ? 4 - � � & 4 � - 4 ? � ' � � � � � 4 � ) ? � )$ � � $ � � ) " A � � � V ? � ' A ' � � � 8 : � � E � � � � : � H � � � � ) � � � $ � ' & 4 � � 1 � � 1 � � � ' ? � )$ � � ) � � � ' I 4 � � ' � ? � � � I � 4 � ? � � � 4 � $ � 1 � ) I 4 � � � � � C � � � � 8 & � � & 4 � � 1 � � 1 � � � '

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Page 5: Simulation of Simultaneous Events in Regular Expressions

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: & % i " j @ J @ . % 2 = $ * + / 6 % @ . & $ % % , " ( ( . " ( % @ ; : & % $ % Y . / $ % 2 % ( . @ = % & / X & " . / * ( * $. & % i % . " W o + % ( . r % X ( / . / * ( s " ( ( . " ( % 0 i o r s 1 3 C " @ % 6 * ( " ( % T . % ( @ / * ( * ) ", / ( % " $ . % 2 = * $ " , , * ( / & 0 s : s 1 | } ~ � 3 " , , * R @ . @ . * % T = $ % @ @ " , " $ ( % @ . C @ % . * ) @ " ) % . J= $ * = % $ . / % @ * ) @ J @ . % 2 @ 3 / ( & , . 6 / ( ( $ % " , W . / 2 % = $ * = % $ . / % @ ; : & % 2 * ( / . * $ / ( ( @ & $ / = . 3% T = $ % @ @ % 6 / ( . & % L $ / 2 / . / + % o + % ( . r % X ( / . / * ( s " ( ( . " ( % 0 L o r s 1 3 / @ . @ % 6 . *

6 % X ( % R & " . / ( ) * $ 2 " . / * ( / @ @ % ( . ) $ * 2 " X , . % $ . * . & % i " j @ J @ . % 2 " ( 6 & * R / .

/ @ . $ " ( @ ) * $ 2 % 6 / ( . * % + % ( . @ " ( 6 & * ( 6 / . / * ( @ . @ % 6 / ( i o r s ; : & % @ . % % $ / ( ( @ & $ / = .

R $ / . . % ( / ( . & % � . % % $ / ( ( � & . / * ( r % X ( / . / * ( s " ( ( . " ( % 0 � � r s 1 / @ . @ % 6 . * @ = % & / ) J" & . / * ( @ . * C % / ( + * d % 6 R & % ( + / * , " . / * ( @ * & & . $ ; � % % | � 3 } � � ) * $ L o r s " ( 6 � � r s6 % . " / , @ ;

? @ ? @ N O P 5 / 1 J C / R D > / R 2 1 2 > / J

O P 5 / 1 J * & & . $ / ( @ . " ( . " ( % * . @ , J 6 . $ / ( ( . & % @ J @ . % 2 % T % & . . / * ( 3 R & % $ % " @ 6 > / R 2 1 2 > / J

$ % = $ % @ % ( . / ( ) * $ 2 " . / * ( . & " . & * , 6 ) * $ " 6 . $ " . / * ( * ) . / 2 % ; � * $ % T " 2 = , % 3 " ( % + % ( .

6 % ( * . / ( ( . & % & " , , . * 2 % . & * 6 Y ( Y * & & . $ @ " . . & % / ( @ . " ( . . & % & * ( . $ * , / @ = " @ @ % 6. * . & % 2 % . & * 6 3 R & / , % " & * ( 6 / . / * ( � � ( [ \ � ^ _ ` � & * , 6 @ " @ , * ( ( " @ . & % + " , . % * ). & % + " $ / " C , % � ( [ \ � 6 * % @ ( * . % T & % % 6 _ ` ; : & % @ J ( . " T * ) % + % ( . @ " ( 6 & * ( 6 / . / * ( @

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Page 6: Simulation of Simultaneous Events in Regular Expressions

� � � � � � � � � � � � � � � � � � � � � � � � � � � !

� # # � � & � ( � * � & ,

� � � � � � � � � � � � � � � � � � � � � ! ! � � � � � � � � ( ) � � �� � � � , � � � / 1 � � � � � � � 5 � 8 � � � ; � � � ! ! � � � � � � � � @ �

� � ( � � * � / � 1 � � � � 1 � � 3 � # 5 # � 7 � � � 3 � � � # / � 7 1 � � 7 � � � � � # / = � 7 � ? � � 7 � � � � � 5 # 5 / *& / A , C 3 � � � # � � � E , F / � 7 � � � E , F / = � � = � G G � = � 7 & � � � , ( � 1 � � # � = 5 � / � 7 L / * # � O= � # P � 1 � � 3 � * A , R � � 3 � � � � ( ) � � , � # � = � G G � = � 7 & � � � � � # � = � G G � = � 7 / � 7 , � # � = 5 � ,R 1 � � 7 � � � � � � � / 1 � � � E , F � # � = 5 � & � � � , � # 7 � ? � � 7 , R 1 � � 7 � � � � � X � J L � N F � # � = 5 �

( � � & � � � � � � � 1 1 5 = = � � 1 � � L � 3 � � � # � J / � 7 � N & � � = � � J � # � � 1 * 5 7 � 7 ( 5 � � N � # � � � ,Z � = L � = / * # � / � � � 1 # � L � 3 � � � # / � 7 1 � � 7 � � � � � # O # � � X _ O ` ` a ,

O P O P O Q R S U V W R X S Z R ] X ^ S ^ ` X b U X d e U d R f Q V Z b hc C d f � � 1 * 5 7 � # � 3 � � � # / � 7 1 � � 7 � � � � � # � P � = � � 7 L = � i C d f O 7 � ? � � � � � � # � L

1 � P � # � � � � 3 � � � # / � 7 1 � � 7 � � � � � # O # / L � � A P = � P � = � � � # O / 5 k � * � / = A 3 / = � / ( * � # O / � 7/ 5 k � * � / = A L 5 � 1 � � � � # , R # / L � � A P = � P � = � A 1 / � ( � � k P = � # # � 7 / # / 1 � � 7 � � � � � � =/ # / � � 3 � � � 1 / * * � 7 / � / * / = , R # / L � � A P = � P � = � A 1 � � 7 � � � � � 5 # � U k m U o p ( �

� = 5 � 7 5 = � � G � � � � k � 1 5 � � � � & � � = � / # / � / * / = 5 # � X R W R s ( � = / � # � 7 , R 5 k � * � / = A3 / = � / ( * � # 1 / � ( � 5 # � 7 � � 7 � ? � � � 3 � � � # / � 7 1 � � 7 � � � � � # , R 5 k � * � / = A 3 / = � / ( * � # / * * � &5 # O L � = � k / P * � O � � 1 � 5 � � � � � � 5 ( � = � L � 1 1 5 = = � � 1 � # � L / � � 3 � � � , R 5 k � * � / = AL 5 � 1 � � � � # / = � � 1 v � E � F / � 7 x y z � E � F O & � � 1 � = � � 5 = � � � � � � � # � / P / � 7 � � �

3 / * 5 � � L / � � 3 � � � � O = � # P � 1 � � 3 � * A ,

{ | } = > ~ � ~ = @ | � � ~ = > A C � D � � � � � � � �

� � # # � 1 � � � � 7 � # 1 = � ( � # � � � � k � � � # � � � � L � � � c C d f * / � G 5 / G � � � � � 1 * 5 7 � � � �

# P � 1 � ? 1 / � � � � � L � � � � = 7 � = � � G � L � 3 � � � # ( A � k P = � # # � � G � � � / # / = � G 5 * / = � k P = � # z# � � � / � 7 / L = � { 5 � � 1 A � L � 3 � � � # � � / � � � � � � � = 3 / * ,

� P � � o X S U �

f � � � ( � / # � � � L = � G 5 * / = � k P = � # # � � � � / � # O � , G , O � L � J L � N O � � 1 , f � � � ( �

# � / � � � � � # � � � � � c C d f z ~ C O � � � � � ( � � � � � k � # � � � G c C d f # � / � � � � � # O  � ( �

/ * � # � � L � 3 � � � # O ¡ ( � = � G 5 * / = � k P = � # # � � � # O / � 7 � ( � � � � 1 � � 7 � � � � � # 7 � # 1 = � ( � 7 � �

� � 1 � � � � � , � , ` , ¢ � 7 � ? � � � � � # A � � / k � L � � � c C d f z ~ C � k � � � # � � � / # L � * * � & # ,

£ ¤ ¤ ¦ £ � � � � L M N P R N S T U L V W P R Y R [ ] [ S R P¨ © ª « ­ ®¯ ± ³ µ ¶ · ¸ [ ^ U L V W _ a L P R Y R [ ] [ S R

¶ ¤ ¤ ¦ ¯ ¨ ¶ ¹ ¶ ¨ ¶ º ¶ ¨ ¶ » a [ T d e Y f [ M g f [ P P N h S P

¯ ¤ ¤ ¦ ¼ ¨ ½ ¿ À Á ¿  à Š¨ Ç È É Â Ã Å L M N P R N S T [ i [ S R P¨ ¯ Ë Ë ¯ ¨ ¯ ¨ ¨ ¯ ¨ ¯ Ì Í Ç È Ã¨ ½ ¿ À Á ¿ © ª Î ¶ Ï ¨ ½ Ñ Ò Ò Ç ½ ½ Î ¶ Ï ¨ Ó À Ô Õ Î ¶ Ï a [ T d e Y f [ M g f [ P P N h S [ i [ S R P

� ¤ ¤ ¦ ¿ Ô � Ç Â ¯ Å ¨ � À Õ Ñ Ç Â ¯ Å ¨ � Ò Ò Ñ Á Â ¯ � Ã Å k d M N e N Y f l m d S o R N h S P

� � c C d f z ~ C � k � � � # � � � � � 1 * 5 7 � # = � G 5 * / = � k P = � # # � � � # O � 3 � � � # � � � � E ¡ F O z Ö Ö � E ¡ F O / 1 y E ¡ F O / � 7 / � / 5 k � * � / = A L 5 � 1 � � � � × Ö Ö z � E � L � F , � � = � G 5 * / =

� k P = � # # � � � # O = / � G � 7 � 3 � = / # � � � L � 3 � � � # O 1 � � # � # � # � L � 3 � � � # E � F O 1 � � 1 / � � � / � � � �

Page 7: Simulation of Simultaneous Events in Regular Expressions

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$ � & � ' ) * 2 4 6 2 $ � � � ' ) , 2 . � 0 8 8 2 8 2 : , 4 $ � � ' & < > 8 8 8 8 2 : � � � � ! $ � ' 4 2 . 4 < , : 8 2: > , : @ 8 2 : , 4 : 6 C 2 8 4 8 4 2 E : > 8 4 8 E * 0 , 4 8 G H 4 8 2 2 4 6 2 & < > 8 8 8 8 2 : � � � � $ � ' 4 2 . 4 < , : 8 2: > , : @ 8 > , 8 8 M 6 * 2 . , 2 8 P * 8 2 < 8 6 M 8 8 8 2 : 2 : > , : 2 H 8 < 4 S 8 2 : > 8 4 8 E * 0 , 4 8 G H 4 8 2 2 4 6 2 ), 2 . : > 8 8 8 8 2 : � � � � $ � ' 4 2 . 4 < , : 8 2 : > , : @ 8 > , 8 8 2 : , 4 : 8 . 6 C 2 8 4 8 4 2 E C * : M , 4 0 8 . : 6

S 2 4 2 > S 2 . 4 2 E 2 * < > , 2 8 P * 8 2 < 8 & [ 6 4 , 2 8 8 8 2 : ! , 2 . , < 6 2 . 4 : 4 6 2 # ) : > 8 , * G 4 0 4 , 4 ]M * 2 < : 4 6 2 % � � � � $ ! ( # ' 4 8 : * 4 2 2 , M 4 8 P * 8 2 < ] 6 4 , 2 * S C 8 4 6 M 6 < < * 4 4 8 2 < 8 2 6 M , 2

8 8 8 2 : ! . * 4 4 2 E : > 8 : 4 S 8 4 2 : 8 4 8 , 0 @ > 8 2 # > 6 0 . 2 : 4 * 8 &

* + - . / 0 1 2 4 5 7 8

c 8 : � � 4 2 [ 4 E & e . 8 2 6 : 8 , 2 8 : 6 M 8 8 8 2 : 2 2 H 8 < 4 S 8 . 4 2 , f # : , 2 . � # . 8 2 6 : 8

, < * 2 : 6 S 4 h 8 . 2 8 : 6 M 8 8 8 2 : 2 2 H 8 < 4 S 8 . , 2 <! 4 2 : > 8 2 8 @ j # l c m f # 2 : , : 8 S 8 2 :

2 > 6 @ 2 4 2 : > 8 2 ] 2 : , G 2 8 < : 4 6 2 & < > 8 2 ) , 4 8 0 8 8 , 2 : 8 8 8 2 : 2 8 : 6 M : 4 2 � � � � �� # & ? 8 S 6 . 4 M ] : > 8 S 6 . 8 0 ' . 8 S 2 8 . 4 2 t u v , 2 M 6 0 0 6 @ 2 & w S 6 . 8 0 ' 4 2 , : * H 0 8

$ * ( , ( . 0 ( . � ( 1 ' ) @ > 8 4 8 * � � B 5 ( B D ( 6 6 6 � 4 2 , 2 8 : 6 M 2 : , : 8 2 ) , 4 2 , S , H H 4 2 E M 4 6 S

* : 6 : > 8 : 4 S 8 . 6 S , 4 2 ) . 0 4 2 , : 6 : , 0 M * 2 < : 4 6 2 M 4 6 S * = > : 6 � A � C F ( E G H B F ( I �@ > 8 4 8 > . 8 2 6 : 8 2 , 2 8 : 6 M < 6 2 . 4 : 4 6 2 2 , S 8 2 , 2 . I . 8 2 6 : 8 2 * 2 . 8 S 2 8 . ) , 2 . . �4 2 , H , 4 : 4 , 0 M * 2 < : 4 6 2 M 4 6 S * = P : 6 , 8 , 0 * 8 . 6 S , 4 2 @ > 8 4 8 P . 8 2 6 : 8 2 , 2 8 : 6 M8 8 8 2 : 2 , S 8 2 & [ 6 4 , 0 0 F R @ > 8 4 8 . � $ B T ( F R ' 4 2 . 8 S 2 8 . ) : > 8 4 8 4 2 , 2 6 4 . 8 4 1 $ B T ( F R '2 * < > : > , : , : : 4 S 8 , $ B T ' ) , 2 6 4 . 8 4 M 6 4 8 , < > 6 < < * 4 4 8 2 < 8 F R 4 2 . 4 2 : 4 2 < : & < > 8 6 4 . 8 41 4 2 , : 6 : , 0 , 2 . 4 2 V 8 < : 4 8 8 M * 2 < : 4 6 2 : > , : S , H 2 F R , 2 . B T : 6 , 2 6 4 . 8 4 8 . 2 8 : 6 M

H 6 2 4 : 4 8 8 4 2 : 8 E 8 4 2 , 2 . 1 $ B T Y D ( F R ' [ 1 $ B T ( F ] ' M 6 4 , 0 0 ^ , 2 . , 2 ] ` ) H &

< > 8 2 8 S , 2 : 4 < 2 6 M j # l c m f # 4 2 . 8 S 2 8 . * 2 4 2 E , . 8 4 4 8 , : 4 8 8 6 M , f # t L v & [ 6 4, 2 ] f # : , 2 . , 2 ] , 0 H > , C 8 : G ) , M / N 5 P 1 4 5 P / S b : U 5 4 V N / 8 d / 7 4 4 S 1 ) . 8 2 6 : 8 .C ] f g $ : ' ) 4 2 : > 8 f # ) @ > 8 4 8 f g $ : ' � � j l � n Y G j l : � & [ 4 E & � , 2 . [ 4 E & �2 > 6 @ : > 8 2 8 S , 2 : 4 < 2 6 M , . 8 4 4 8 , : 4 8 8 6 M , f # , 2 . : > 8 M * 2 < : 4 6 2 ! $ : ' M 4 6 S � n

: 6 r 1 1 H F G t ) @ > 4 < > : 8 2 : 2 @ > 8 : > 8 4 u l : ) 4 8 2 H 8 < : 4 8 8 0 ] ) @ > 8 4 8 : D ( : \ , 4 8 4 8 E * 0 , 48 G H 4 8 2 2 4 6 2 2 ) G ( r l � , 2 . G x� r &

� 8 2 4 . 8 2 : > 8 . 8 4 4 8 , : 4 8 8 2 ) @ 8 , 0 2 6 2 8 8 . : 6 . 8 S 2 8 , M * 2 < : 4 6 2 z { | } $ : ' , 2 . ,M * 2 < : 4 6 2 ~ � ] $ : ' & z { | } $ : ' 4 8 : * 4 2 2 , 2 8 : < 6 2 : , 4 2 4 2 E , 0 0 8 8 8 2 : 2 : > , : < , 2 , H H 8 , 4

, 2 : > 8 S 4 2 : 8 8 8 2 : 4 2 : > 8 f # : & [ 6 4 S , 0 0 ] ) z { | } $ : ' � � G l � � � u � Y G j l: @ > 8 4 8 j l � n � & ~ � ] $ : ' 4 8 H 4 8 2 8 2 : 2 : > 8 4 8 S , 4 2 . 8 4 6 M : > 8 f # : , : , 2 6 4 . 8 41 , M : 8 4 , 2 8 P * 8 2 < 8 6 M . 8 4 4 8 , : 4 8 8 2 & ? 8 . 8 S 2 8 ~ � ] $ : ' , 2 M 6 0 0 6 @ 2 &

� � � � � � � �] a � b c � � � � � � a d T b e c f � � � � � f � � � g � � a � b� � � � � � � �] a � b c � � a � � � � � � � � Y D

] a � b b � � � � � a d T b e c f

? 8 , 0 2 6 . 8 S 2 8 , 0 , 2 E * , E 8 � $ : ' 6 M : , 2 M 6 0 0 6 @ 2 &

� a   b c   � a ¢ b c ¤ ¢ ¦

L

Page 8: Simulation of Simultaneous Events in Regular Expressions

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� � � � � � � � � - 3 � # - � � � 6 . 0 � 3 0 � � . 0 0 � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �

� # 9 ; % � " $ & ' � ) + ; - ( * � ' � ) / 0 < - < 2 ; < ? @ < � � � � � " , ' � ) < 3 < ; ? / � � ! ! $ � � ' � )< 3 < ; ? / + ; - ? @ < ' � ) * ' � ) < 3 < ; ? 7

- / 1 � � , . / 0 . 2 3 � � � � 3 - / 1 � � 4 . 0 � 4 � 7 9 2 : ; � � �

- / 1 � � , 6 7 7 8 , , � � � � 3 - / 1 � � 4 � - � � � 7 9 2 : ; � � = � > * @ A C D = F G �� � � � � � . 0 � � H � ; I �

- / 1 � � < / = ? � � � � 3 - / 1 � � 4 � - � � = � > * @ A C D = F G �� � � � � � � . 0 � � H � ; I �

F @ < < 3 < ; ? � � � � � " , ' � ) 9 # ? ; 9 % % < ; < - 0 @ < ; + ; J ? ? @ ; 9 ; % < 3 < ; ? 9 # J ; < J B ? @ < < 3 < ; ? #? @ + ? ? + ; + E E < + ; + # ? @ < 2 ; # ? < 3 < ; ? 9 ; ? @ < G I � 7 F @ < < 3 < ; ? � � ! ! $ � � ' � ) 9 #? ; 9 % % < ; < - 0 @ < ; + ; J ? ? @ ; 9 ; % < 3 < ; ? C ? + @ # < # ? @ < - < ; 9 3 + ? 9 3 < J B ? @ < ; < U + 9 ; - < ; ? J

? J ; ? + 9 ; < U E ? O # ? ; 9 ; % / + ; - ? @ < < 3 < ; ? ' � ) * ' � ) 9 # ? ; 9 % % < ; < - 0 @ < ; + ; J ? ? @ ; 9 ; %< 3 < ; ? C ? + @ # < # ? @ < - < ; 9 3 + ? 9 3 < J B ? @ < ; < U + 9 ; - < ; ? J Q < ? J U < @ ; - < 2 ; < - 7

N < R ? / 0 < - < 2 ; < + B ; < U @ < ; ? O B @ ; ? ? 9 J ; D ! ! � � ' C E G ) 7 X B @ ; ? ? 9 J ; D ! ! � � ' C E G ); < ? @ ; ; # ? @ < ; @ U Q < ; J B J ? ? @ ; ; < ; ? < # J B + ; < 3 < ; ? C - @ ; 9 ; % ? @ < ? 9 U < 9 ; ? < ; 3 + Z ? @ + ?

+ ? J ; - 9 ? 9 J ; G @ J Z - # ? ; @ < 7 D ! ! � � ' C E G ) 9 # - < 2 ; < - + # B J Z Z J 0 # 7 ] < ? P ' N I E C E G ) - < ; J ? <

+ B ; < U @ < ; ? O J B C 9 ; G + ? ? 9 U < S ' N I ) 7 X ? ? 9 U < S ' N I ) / D ! ! � � ' C E G ) R V ' N I E C E G ) 7

W � ; I / 4 / Y � � � � � - / H � ; I � \� � Y� ] � � - / H � ; I � � � ; 1 � S 1 � Y �

� W � ; I G � / 4 / Y � � � - / H � ; I � � � Y � - � - / H � ; I � \� � 4� W � ; I G � / 4 / Y � � U � � - / H � ; I � � � Y � - � - / H � ; I � � � 4

V W V X Y Z [ ` \ ^ _

F 0 J < R + U E Z < # J B ; < U @ 9 ; < U < ; ? # ? @ + ? ; < < - # @ ? @ ? 9 U 9 ; % - < E < ; - < ; ? 9 < # + ; <

' 9 ) Z a ^ d ^ a e b [ f _ e a g e g i i f j e m j ^ ^ e n [ ^ _ n a Z j g q c + ; -

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Page 9: Simulation of Simultaneous Events in Regular Expressions

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" � � $ � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � " � � � � � � � � � � � ' ( � �

* � � � � � � � � ' � ' � � � � � " � � � � � 2

% ' � � � ) + - � 4 / 5 / 7 / � / � / + � 2 � 4 � � - � � ' � � � ) 4 + � 2 5 + - � � � � - � 9 + � � 2 � � � ' � � � )7 / � / � / + � 2 � / + � 2 ' � ? � ' � - ) + B � � ) C � ? � E G � � � ) � - � I J � - � � � � � ) � � � � � � L � ) � � � M

N % Q S / 4 � � � � 2 + E � 4 + J L � 9 � + - G ' + - � + X 9 � ) � � Y � � C � - + ? Y � E 4 � � � + � 2 � � 4 � + � G� � � � ) � ' � � � ) 4 / 7 / � / � / + � 2 � � ? ? J - B � � � E - + M � � � � � E N % Q S X � 9 � 4 ) � � 4 ) � � 44 � ) C � ? � E G � � � + X � ' � - � I J � - � � � � � ) � � � � � � - � M � � + 9 N % Q S B

< 4 = 4 � ? A C D F 7 � � � � ? A C D �

4 G 4 = I 4 K � 4 7 M N C 4 � ? A C D � � K �

N < N C D 7 � � � � R � $ $ � 7 M N C T 7 F � W W $ $

R � 7 M N C T 7 F N C Y R T � F � W W W W 7 M N C ] �

^ = ? ^ N = D � 7 � � � * _ � 7 � � � � ? A C D ` * _ �

4 - . / 4 � ? A C D 0 � 4 � ? A C D 3 * � 6

5 - . / 4 � ? A C D 0 � _ � 6

7 � � � - . / 7 � � � � ? A C D 0 � 7 � � � � ? A C D 3 * � 6

� � � 4 � ? A C D ' + - � + X 9 � Y � � C ) � - + ? Y � E � � 4 � + � G � � � � ) + � � ' � � � 4 � ? ? J - ) B d � � � d� ' � - 4 � ? ? J - ) / 4 � � � ? - � � � � � � � + � 2 4 � � � � ' � - 5 � ? ? J - ) / 4 � - � ) � � � � B � � � + 9 + - �

4 K + 9 � - � ) J ) � - ) 4 � � � 4 � ? A C D X � ? � � � ) i B � � � � ' � � � 7 � � � � ) � - � M M � - � 2 � � 9 G4 � � � ] � � 9 2 ) � - J � + � 2 4 � � � � � - � � ? ? J - ) X � � 4 � � � 7 + � 2 � � - 4 � � � � � ? ? J - )X � � 4 � � � � + � 2 � B � � � 7 � � � � ? A C D ' + - � + X 9 � ) � � - � ) � � � � J � X � - � E � � � � ) � � �

� ' � � � 7 � � � � + ) � ? ? J - � 2 B � � � C - � C � - � G 7 � � � * _ + 9 � - � ) J ) � - ) 4 � � � 7 � � � � ? A C D

� ) M - � + � � - � � + � n o B

p � � ) � 2 � - 4 � � � 4 � � � � 2 � � ) C � ? � E G � � � � - 2 � - � � M � E � � - � � � + � E � J - � ' � � � ) / � � �

� ' � � � ) J ? � + ) 7 � � � ? + � M � � ' � - G ? � � C 9 � ? + � � 2 X � ? + J ) � � � � � + � G ? + ) � ) � � � 2 � �

X � ? � � ) � 2 � - � 2 B � � � ) ) � � 4 ) � � + � 4 - � � � � M - � I J � - � � � � � ) J ) � � M � � � � L � ) � � � M N % Q S� ) � - - � - d C - � � � + � 2 2 � y ? J 9 � � � J � 2 � - ) � + � 2 B z G + 2 2 � � M - � M J 9 + - � L C - � ) ) � � � ) � �

� � � 9 + � M J + M � / + � � - 2 � - � E � ' � � � ) ? + � X � � L C - � ) ) � 2 � � - � � � � J � � � ' � 9 G B � � � X � 9 � 4E - + M � � � � � E � � � ) C � ? � | ? + � � � � ) � � 4 ) � � 4 � � ) C � ? � E G � � � � L + � C 9 � - � I J � - � � � � � )� � � � � � L � � � 2 � 2 N % Q S d } % B

h i j > h i l @ m n p j B j B j q Ch i r D F H h i l m n p r B D B F B H q C

j s j t J j > n u v w w x u u y j > h i z C

K t L K x t { F r D F H N P n L w w v t y � j � s y r D F H h i z Q w z p N P C

� � � - � M J 9 + - � L C - � ) ) � � � 4 K S T + � 2 7 � � � S T 2 � � � � � � � � � - 2 � - � � M � E � ' � � � ) 4 � ? d? J - - � � M � � - � � � � � � ) � � + - � 4 + � 2 � � � � - 2 � - � � M � E � � � � ' � � � 7 E � 9 9 � 4 � 2 X G � � �

� ' � � � ) � / � / + � 2 � B � � � - � 9 � ' + � � ) � � / 5 6 � � 4 K S T � � 2 � ? + � � ) � � + � � E + � � ' � � �

5 � ? ? J - ) X � � 4 � � � � 4 � � ' � � � ) 4 / � � � � � � � ) ) � I J � � ? � 4 � J 9 2 E + � 9 � � � + � ? � 4 K S T B� � 4 � ' � - / � � � N % Q S d } % 4 � J 9 2 � M � � - � + � � ' � � � � � E � � � ? ? J - ) X � � 4 � � � � 4 �

� ' � � � ) 4 + � 2 4 � J 9 2 � � � E + � 9 � � � ) � I J � � ? � B � � � - � 9 � ' + � � ) � � / 6 � � 7 � � � S T 4 � - Y )) � � � 9 + - 9 G B � � � + 9 + - � 4 K + 9 � - � ) J ) � - ) 4 � � � 4 � ) J ? ? � ) ) E J 9 9 G � + � ? � � � � } % 4 K S T

4 � � 9 � � � � C - � C � - � G 7 � � � * _ + 9 � - � ) J ) � - ) 4 � � � � � � } % 7 � � � S T E + � 9 ) � � - � � � + �

� � � � � � � ) B � � � - � I J � - � � � � � ) � � 4 + - � � J ? � ) � � C 9 � - + � 2 � + ) � � - � � J � 2 � - ) � + � 2� � + � � � � � - � M � � + 9 N % Q S B

Page 10: Simulation of Simultaneous Events in Regular Expressions

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� � � � � � � � � � � � � �

" � � $ � % � ' � � $ % � $ � % � + � - � � � � � % � / 1 � 1 ' 4 5 � + � � � � � � � % � ' % / � � 1 + 1 � � � 1' 1 � 9 : � � � 5 + ' � > @ A : C 5 + ' 1 $ � 1 1 4 5 � A 1 � / � � � ' 5 1 + 1 � � � % � 1 � A % : � 1 H � � � : � IA 1 � / ' > � � � % � � 1 � : L � � � ' A � � � ' � � � O Q S " U � � � � � � � % ' W X 1 $ % � - � % % � >� [ � % ' � � � \ > � � � % � � 1 � : L � � � ' A � � � ' � � � O � S " U H _ � [ � % ' 5 � ` 1 � � / ' 5 / � % � 4 � 14 ' [ � 4 � � � $ % � $ � 1 � > � � � 9 : � � � 5 + : � � 1 � % A : � ' � > � � � b � ' Q S " - % � � ' / [ � �

W X H � 4 ' [ � : 4 � 1 � � � 4 � ' 5 / � % � 4 � 4 + " 4 � I _ � � 4 ' � > � 5 5 � ' � k l m 4 � : ' A 1 � �

/ � � � % ' � � 1 ' Q S " > % � : � 5 + q � 4 � A � / � � � % ' � � / ' � � S " H 9 4 � � � $ % : ' 5 % � 1 A 5 � 4 + ' � 1 � � k u � m ' 5 1 � 1 A / / � 1 � 1 � 4 ' � � 4 1 Q S " : � � 1 � % A : � � � 1 � 9 : � � � H

_ � A 5 ' � � � � - ' Q S " � [ � 5 [ � 1 � 4 � - � 5 5 � q � / 1 � � $ 1 H x > � � � - + ' W X � 4 ' � 4 ' 1� 4 � : A % % � � � � [ � � � � � 1 % � 5 � [ ' � � 1 � � H 9 4 � � : � � $ ' % � � 4 � : A % % � � � � [ � � � q � 4

' 5 5 � 4 � $ � 1 1 4 5 � � % ' � 1 � � � 1 - % � � � 4 � : A % % � � � 1 � ' � � � - � 4 � Q S " ' � > � ' C � � 4 �

' $ $ % � $ % ' � � � � � H x - � 4 � : A % % � � � � [ � � � � � ' � � 1 � 4 � 1 � A 5 ' � � � � - ' Q S " I � 4 � �

� q � A 5 > � % / / � % ' � � � � � � � [ � � � H x - � 4 � ' A � � � ' � � � � � [ � 1 � � ' L � ' 5 1 � ' � � I ' � � � � � [ � � � 1 � % / / � % � > A � > � % : � % � ' � : � � > � � � 1 ' 1 1 $ � : L � > � _ � : � � � � H

_ � 5 ' % 5 + I � 4 � � [ � � � : ' A 1 � / � 4 � ' A � � � ' � � � � � / � � 1 � A : C � % / / � % 1 ' � � � � � [ � � � H� � q � [ � % I � 4 � $ % � 4 5 � � � Q S " 1 � A 5 ' � � � ' % 1 � 1 q 4 � � � 4 � % � ' % � 1 � A 5 � ' � � � A 1

� [ � � � 1 / � � � % ' � � > 4 + � � � $ % � � [ � � [ � � � � % : � � > � � � H _ � : � � 4 � % � 1 � � � 4 � % � � �

� % > � % ' � � � / 1 � � 4 � 1 � 1 � A 5 � ' � � � A 1 � [ � � � 1 I � 4 � Q S " 1 � A 5 ' � � � � A 1 � � [ ' 5 A ' � �

� A 5 � $ 5 � $ ' � 4 1 1 � A 5 � ' � � � A 1 5 + - � % ' 5 5 $ � 1 1 4 5 � $ � % � A � ' � � � 1 � - � 4 � 1 � � [ � � � 1 H9 4 1 1 � ` $ � � 1 [ � � � � % � 1 � - % � 1 � A % : � A � 5 b ' � � � ' � > � ' + ' 5 1 � 4 � � � � \ [ ' 4 5 �

- � % : � % � ' � ' $ $ 5 : ' � � � 1 � 1 $ � : ' 5 5 + � % � ' 5 � � � 1 + 1 � � � 1 H

� ! # $ & ' & * � + , - $ 0 2 # 4 ' * $ & 6 7 ' 4 2 &

9 4 � � ' � 5 ' � / A ' / � : � � 1 1 � 1 � - 4 / 4 \ 5 � [ � 5 � % : � � $ � 1 � � � [ � � � 1 ' � > : � � > � � � 1 I' � > 5 � q \ 5 � [ � 5 � % $ % � � [ � � [ � � � 1 ' � > : � � > � � � 1 > � 1 : % 4 � > � _ � : � � � l H u' � > l H l H 4 � � $ % � � [ � � [ � � � 1 � % : � � > � � � 1 ' % � > � � � : � � > I � 4 � L 5 � � % 1 � � > 1

� 4 � � � � � 4 � � [ � � � % � : � / � b � % � � 4 � � % > � % ' 1 � 4 � + � : : A % H 9 4 � 1 � $ % � � [ �

� [ � � � 1 ' � > : � � > � � � 1 : ' � � % / / � % : � � $ � 1 � � � [ � � � 1 � % : 4 ' � / � � 4 � [ ' 5 A � � -: � � > � � � 1 H 4 5 � � 4 � $ % � � [ � � [ � � � 1 ' � > : � � > � � � 1 ' % � � % > � % � > I q � : ' � \� � � � % > � % � 4 � : � � $ � 1 � � � [ � � � 1 � % / / � % � > 4 + � � � $ % � � [ � � [ � � � � % : � � > � � � 14 � : ' A 1 � ' 5 5 � - � 4 � : � � $ � 1 � � � [ � � � 1 � : : A % ' � � 4 � 1 ' � � � � � H

_ � : � W X 1 : ' � 4 � > � L � � > � � : � � $ � 1 � � � [ � � � 1 � 4 ' � : ' � � : : A % � > [ > A ' 5 5 +' � > 1 � A 5 � ' � � � A 1 5 + I q � � � � > ' q ' + � � % � : � / � b � � 4 � � [ � � � 1 � 4 ' � : ' � � : : A %1 � A 5 � ' � � � A 1 5 + H x - � q � � [ � � � 1 : ' � � : : A % 1 � A 5 � ' � � � A 1 5 + I � 4 � � � 4 � % � % > � % 1 � 1 / � L : ' � � ' � > � 4 � % : � � : ' � � � ' � � � : ' � 4 � $ � % � A � � > q � 4 � A � : 4 ' � / � / � 4 �

� � ' � � / H 9 � 4 ' � > 5 � 1 � A 5 � ' � � � A 1 � [ � � � 1 � � ` $ � � 1 [ � 5 + I q � $ % � $ � 1 � � 4 � - � 5 \5 � q � / 1 � � $ 1 H Q A % � / � 4 � 1 � ' � : $ 4 ' 1 � I q � > � � � % � � � - � [ � � � 1 A 1 � > � � 4 � W X 1: � A 5 > � : : A % 1 � A 5 � ' � � � A 1 5 + H x - 1 A : 4 � [ � � � 1 � ` 1 � I q � ' A / � � � � � 4 � � % / � ' 5 Q S "

q � 4 ' 5 � � % � ' � [ � � % ' � 1 � � � 1 H " � % A � � � � I q � � % + � � � ' C � ' 1 � � $ A 1 � / � 4 � � % / \� ' 5 � % ' � 1 � � � 1 H x - � 1 � � � $ � 1 1 4 5 � I q � � % + � � � ' C � ' 1 � � $ A 1 � / � 4 � ' 5 � � % � ' � [ �

� % ' � 1 � � � 1 � � 5 + - � 4 � % � � ` 1 � 1 ' 1 � � � - � [ � � � 1 - % � � ' � � � / � 4 � % � 5 � [ ' � � 1 � � � -� 4 1 W X � 4 ' � 4 ' [ � � : : A % � > 1 � A 5 � ' � � � A 1 5 + H

Page 11: Simulation of Simultaneous Events in Regular Expressions

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� � ! " $ & $ ) & + - . / + 0 2 4 & 7 - $ 9 2 < = > $ - & <

+ , # - / - % / ' , ( ( 4 + - - ( 4 7 / - / 2 9 - , / ( - 4 - 9 / ( ( / 2 / 4 % 2 - - 8 9 : - % , 9 ( / < / % / 2 # - ' - 9 # - 9 % 8> < 2 ' > @ < , 7 / > - ( 8 9 / 2 E , @ - 4 - 9 / ( 2 9 # % , 9 # 4 / 4 , 9 ( / ( 4 9 > % , 9 9 - % / 4 4 - ( # - ( % < 4 + - # 4 9

L - % / 4 , 9 M N + > - # - ' - 9 # - 9 % 8 > < 2 ' > � @ Q � B D R 4 ( 2 # 4 < - % / - # > < 2 ' > : > - < - / > -

4 - < / 4 % - ( � 2 < - % , 9 9 - % / 4 4 - ( 9 - 4 - 9 / ( 9 2 9 # % , 9 # 4 / 4 , 9 ( 9 2 9 # / > - - # > - ( D < - ' < - ( - 9 /

# - ' - 9 # - 9 % 8 + - / : - - 9 / > - 7 N Y - / F G 9 F I + - - 4 - 9 / ( , < % , 9 # 4 / 4 , 9 ( N + > - 9 9 Q F G B F I R !

D 4 @ 2 9 # , 9 - 8 4 @ F G 4 ( / ( - # / , % , 7 ' , ( - F I N ` , < - E 2 7 ' - - 9 4 @ F # @ F G L L F I 9 / > - 9

Q F G B L L R 9 Q F I B L L R 9 2 9 # Q L L B F # R 2 < - 4 9 D N ` 4 > N P ( > , : ( 2 9 - E 2 7 ' - - 7 , 9 4 / , < 4 9 > ( % < 4 ' / 92 9 # ` 4 > N Q ( > , : ( / > - % , < < - ( ' , 9 # 4 9 > # - ' - 9 # - 9 % 8 > < 2 ' > N g 9 / > - h > / < - ( 9 / > - < - 2 < -

/ : , ' < 4 7 4 / 4 4 - - 4 - 9 / ( S T U V W Y Z $ & ( \ 9 S T U V W Y Z $ & * \ 2 9 # / : , ' < 4 7 4 / 4 4 - % , 9 # 4 / 4 , 9 ($ & ^ , 9 $ & ^ - N k - - , @ / > - 7 2 < - 4 - < / 4 % - ( 2 / / > - + , / / , 7 , @ ` 4 > N Q N L 4 9 % - / > - - 4 - 9 /

S T U V W Y Z $ & ( \ 2 9 # / > - % , 9 # 4 / 4 , 9 $ & ^ , 2 < - / ( - # / , % , 7 ' , ( - 2 % , 9 9 - % / 4 4 - a b Y c 9- # > - ( Q S T U V W Y Z $ & ( \ 9 a b Y c R 2 9 # Q $ & ^ , 9 a b Y c R 2 < - 4 9 D N L 4 9 % - / > - - 4 - 9 / Y , 4 (% , 7 ' , ( - # , @ / > - % , 9 9 - % / 4 4 - a b Y c 9 2 9 - # > - Q a b Y c 9 Y , R 4 ( 2 - ( , 4 9 D N + > - - 4 - 9 / (Y - 9 Y g 2 < - % , 9 ( / < / % / - # ( 4 7 4 - 2 < - 8 N

h - # - 9 , / - / > 2 / 2 9 - 4 - 9 / F I # - ' - 9 # ( , 9 2 9 - 4 - 9 / F G 4 @ 2 9 # , 9 - 8 4 @ / > - < -

- E 4 ( / ( 2 ' 2 / > @ < , 7 2 9 - 4 - 9 / F G / , 2 9 - 4 - 9 / F I 4 9 � N h - 2 - ( , # - 9 , / - / > 2 / 4 @/ > - < - 4 ( 2 ' 2 / > / , - 2 % > , @ F G 2 9 # F I @ < , 7 2 % , 7 7 , 9 4 - < / - E 4 9 / > - > < 2 ' > 9 / > - 9

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Page 12: Simulation of Simultaneous Events in Regular Expressions

� � � � � � � � � � � � � � � � � � � � � � � � � � � !

� � # � % � & & ' % � � � � * & ' * . 0 1 0 � � 3 5 � % � 7 * � : . � ; & � � 0 � = � % � � � # � � 0 � � 5 � > 3 � 3? * 0 � = � � � � = � : � � = � � & 1 > % * : � ; � � � # � � 0 � � * � = � � & * � � & & ' % 0 � � ' . * J

� � � ' 0 . 1 N � & * ' 0 � N � � = � : � � = � � � � � # � � � � � � � � � � 3 R ' : : � 0 � � * � �

& � � = � � � � 0 � � � � * � = � � � � * % � N � � . � * � # * % � * N . � 0 � � � � * % > � : % � > % * � * � = � � 1 * % � � � # � % % ' � * � � 0 * � � � � � 3 , � � � ; � # � � 0 � � * � = � � � � # � % � & & ' %0 � � ' . * � � � ' 0 . 1 3

, � � % � * % � V � 0 : � & � * . & * 0 � 0 3 , � � W % 0 & * 0 � � 0 V � � � * � � # � � � 0 & � � : � 0 � =' 0 � � > * � � � � & � � � � & � # � ] � � � � ^ 3 , � � � # � � V � � � � & � � � � & � # � � 0 % � > J> � % � = � b * � = � � . 1 � b N � � � b � 0 V � * % > ' � � � 0 � � * � = � & � & & ' % 0 � � ' . * � � � ' 0 . 1 3, � � % � b � % � ; � b � � % � � 7 � 0 0 * � & � � � � & � # � * . � � > � � : * � ; � � V � * % > ' � � � 0� b � � & � � � � & � # � � ' 0 = � : � � = � � � � � & � � � � � # � % � 7 3 ) � � % V � 0 � ; � �

� # � � V � � � � & � � � � & � # � V � . . � � # � % N � % � > > � % � = * � = � � % � b � % � ; & * � N �

� . � � � � * � = b % � � : � 0 0 � N . � 0 � � ' . * � � � ' 0 � # � � 0 3 , � � 0 � & � � = & * 0 � � 0 V � � � * �

� # � � � 0 & � � : � 0 � = ' 0 � � > * + , . � & � � � � & � # � ] � 2 3 � 5 6 ^ ; V � � & � & � � 0 � 0 0 � b * �

� # � � 0 � = � � * � = * & � � = � � � � 0 � = � 6 3 , � � � # � � V � � � � 2 3 � 5 & � � � � & � # � � 0 % � > > � % � = � b * � = � � . 1 � b � � � # � � � � & & ' % 0 V � � � � � & � � = � � � � 6 � 0 % ' � 3 n 0 0 ' � �

� � V � � # � � 0 V � * % � = � � & � � > * % � � � * � = � & ; * � = � � � 0 & � � : � 0 � = ' 0 � � > * 2 3 � 5

& � � � � & � # � 3 r b � � & � � � � � # � % � 7 � b � � * � = � & . � � 0 � � � � � # � � 0 � = � � b � � 2 3 � 5& � � � � & � # � � � � � ; � � � � � * � = � & & * � � & & ' % 0 � � ' . * � � � ' 0 . 1 3 r b � . � � 0 � � . 1 � �

� � & � � = � � � � 0 � = � ; � � � � � * � = � & & * � � � � & & ' % 0 � � ' . * � � � ' 0 . 1 3 5 � % � 7 * � : . � ; � � � # � � 0 � � * � = � ? � � 5 � > 3 � & * � � � � & & ' % 0 � � ' . * � � � ' 0 . 1 3 , � � 0 � 0 � � & * 0 �

N � & * ' 0 � � � � � � � � � * � = � � � � � � � � � & * � � � � & & ' % 0 � � ' . * � � � ' 0 . 1 N * 0 � =� � � ' % * 0 0 ' � : � � � � * * . . : % � � � � # � � # � � 0 * % � * . V * 1 0 � % = � % � = 3 A � V � # � % ; � �

� # � � 0 � � * � = � � & * � � & & ' % 0 � � ' . * � � � ' 0 . 1 � b N � � � � � � * � = � � � � * % � % ' � *

� � 0 * � � � � � 3

n 0 � � b : � 0 0 � N . � 0 � � ' . * � � � ' 0 � # � � 0 � N * � � � = N 1 � � * N � # � : % � & � 0 0 & * �

N � ' 0 � = � � = � � � b 1 z { 0 � * V � ' . = % � | ' � % � * ' > � � � * � � � 3 ) � . 1 � � 0 � % � > ' . * %� 7 : % � 0 0 � � � 0 � * � * # � * 0 ' N 0 � � b 0 � � ' . * � � � ' 0 � # � � 0 � � � � � % % � . � # * � 0 � 0� � � = � N � * ' > � � � � = 3

� � � � G I J L � C D G I � N � C E O L J O � G O P H J C N � G L J O � K � L J L �

H J C N � L G O E G N O Q R E O L O

? * 0 � = � � � � � � b � % � * � � � � b 0 � � ' . * � � � ' 0 � # � � 0 : % � # � = � = � � R � & � � � ~ ; V �

� � & � % : � % * � * = = � � � � * . � � b � % � * � � � � � � � � � 5 n 0 * � & * . . 1 3 U � & . * � � � * � � 0* = = � � � � * . � � b � % � * � � � & * � * 0 0 � 0 � � 0 � � ' . * � � � ' 0 0 � � ' . * � � � � b � ' . � : . � : * � 0

� � � � � 5 n � � & � � � . 1 3 , � � b � . . � V � � > * . > � % � � � � 0 : % � : � 0 � = � � � & � % : � % * � � � 0* = = � � � � * . � � b � % � * � � � � � � � � � 5 n 3

� � � � � 5 n N � * � � � � � * . � 5 n > � � � % * � = ' 0 � � > � � * . > � % � � � b � % � 5 n> � � � % * � � � * � = � � � � � � � * � � � * 0 = � 0 & % � N � = � � R � & � � � ~ 3 U � & * . . � � 0 � 5 n * 0� � �

� � � * � = � � * ' > � � � � = � 5 n > � � � % * � = N 1 � � * . > � % � � � * 0 � � � � � � 3 U �

& � � 0 % ' & � � � � � � ' � = � % � � b � . . � V � � > : % � � � 0 � 0 3

] � ^ , � � 0 � � b 0 � � ' . * � � � ' 0 � # � � 0 > � � � % * � = N 1 � � � # � � % � & � > � � � � % = � � 0

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Page 13: Simulation of Simultaneous Events in Regular Expressions

� � � � � � � � � � � � � � � � � � � � � � � � � � � !

� � � " � � $ � � & � � & ) � + ) � " " & . . � " $ � 1 � � $ 3 � 5 � � 6 � � $ 3 $ $ & � + � � � $5 3 ) : < " 3 & $ � � > 3 @ $ B $ � � : � $ � � � . " � . : � � � & � < . � 1 � " " & . . � " $� 1 3 � 5 � � 3 � 3 � B I 5 � � � � $ � 3 � � 6 K � � � ) B . " � . : $ � � + . $ � " � .3 < $ � " � 1 � � 5 � � � " " & . . � " 6

M O � � �� � � " � � $ $ � $ � 1 3 $ � I ) 3 " " + � � I $ � 3 � 6 T � " V : � " � � � ) B � �

$ � � . � $ � $ Y & � " 3 " " + � : < B � � �� � � \ V " 3 � . � � 5 3 ) ) � & � I � � I � . 3 � `

$ � � � $ 1 . � � 3 ) ) � � 3 " " + � � I $ � 3 � $ 6 � � � � � c 3 � � � + . � " : & . V � & ) :� � � � . I � � � $ $ � 3 � $ � � � � � 6

e � � � �� � � � M � � � � � � � � � � O V � . � $ 3 $ � � 1 h � � $ � 3 � $ \ � $ 3 . ) `

5 3 � � 5 � � $ � � 1 � 3 $ : $ " . < : � T " � � � k 6 m \ � � � � � $ 3+ 3 . � 3 ) � . 3 � $ � � � 1 & � " � � � \ � � � � $ � � $ � 3 . � $ � 3 � \ 3 � : � � � � $ � �

$ � I ) 3 " " + � � I $ � 3 � 6 5 � � � �� � � \ � � 3 ) I � . � � � " � � $ � . & " � $ � � � � � �

� M � � � � � � � � � � � � � � � � � � � � O V � . � � � � � � � \ 3 � : � � 3 . � < � 3 � : 1 . � �

� � �� � � \ � � � & � � s � $ � � � � � � � � � � 3 � � � � 3 � � � � 1 3 � . 3 � $ � � � � : `

" 3 � � I � $ ) � � I $ � : $ � 3 � " 1 . � � � � \ � � � & � � s � $ � � ! � � + ! � � � � � � � � �

1 & � " � � � � � 3 � � 3 + $ 3 " � � . 3 � $ � � � � 1 3 $ � 3 � � � 3 & � Y & � 3 � & . 3 ) � & � < .� . c . � \ � � � � � - M � # O $ 3 � � & � � � � � ) � � , 3 � � � � 3 � � � � 1 3 $ � 3 � \ 3 � : � � � � � � � $ 3 + 3 . � 3 ) � / � � ) � � � � & � � ) � � � � � � 7 � 1 & � " � � � 6 : : � � �

M � � ; O � & y M � � ; O (� 3 * 5 M O 3 � : : � � � 7 � � ; � � 8 : � y M � � ; O � � 8 6� � � � � � \ 3 � : � � 3 . : $ " . < : � 1 & . � � . : � 3 ) $ � � � 1 � ) ) � V � I $ " � � � $ 6

� � 3 ) I � . � � � 1 � . � � � � � � " � � $ � . & " � � � � 3 $ � V � + � 3 $ $ � { � � � � 3 � � � � 1 � . 3 � `$ � � � $ 3 � : $ � 3 � $ \ 3 � : I � . 3 � � � � 1 3 ) � . � 3 � 5 � . 3 � $ � � � $ 6

@ ? @ A A � � � @ B C � � 7 � � � � 7 � 7 . C ) � � � � � � 7 � � � � � E � � � � �

| & . � I � � $ + � 3 $ \ V 3 � � � � 3 � 3 " � � . 3 � $ � � � / � � 1 � � �� � � V � � 3

� & � . " 5 3 ) & : � � � : 3 $ � M / O \ $ & " � � � 3 � � � 5 3 ) &

M O Y & 3 ) $ � � : $ � 3 � " � 1 � � � . 3 � $ � � � / 1 . � � � � 3 " " + � � I $ � 3 � � � 6 � � $: $ � 3 � " $ Y & 3 ) � � � � � & � < . � 1 � . 3 � $ � � � $ � � < � . 3 5 . $ : � � . 3 " � � �

1 . � � � � " & . . � � $ � 3 � & $ � I � � $ � . 3 � $ � � � / 6

M O : � � � $ � � � 3 } � & � � 1 3 ) ) $ & " � : $ � 3 � " $ 6

� . 3 � $ � � � $ � � 3 � " � � $ � � & � " B " ) $ � . $ ) 1 ) � � + $ 3 . I � � . : : & . � I � � $ + � 3 $ 6� � $ : $ � 3 � " I � . 3 � � � + � 3 $ � 1 � � 3 ) I � . � � � $ $ � � V � � � I 6 3 6 � � $3 � � � � 3 � � � " 3 � < : � � < B � . 3 5 . $ � I � � | � { & $ � I 3 � � T 3 ) I � . � � � $ � 3 . � � I3 � � � 6

� � $ : $ � 3 � " � 1 � . � 3 � � � � M / O V ) ) 3 $ $ $ � � � . : . � I � 1 � . 3 � $ � � � $ 1 � .$ � & ) 3 � � � 3 � . & � � � 6 : V ) ) � . 3 5 . $ � � � 1 � � � & � I � � I � . 3 � $ � � � $ 1 . � �

� � " & . . � � $ � 3 � < 3 $ : � � � � : $ � 3 � " 5 3 ) & $ 3 $ $ � " 3 � : V � � � � � . 3 � $ � � � $ \ 6 6 \ ) � V . : $ � 3 � " 5 3 ) & h . $ � 6 � � . 3 � � � 3 ) < � � : � � $ " � � " $ � � 3 � � . 3 � $ `� � � $ � � 3 � 3 . " ) � $ . � � � � 3 " " + � � I $ � 3 � $ � � & ) : < 3 � � � + � : < 1 � . � � � $

� � 3 � 3 . 1 3 . � � . 3 V 3 B 1 . � � � 6 K � " 3 $ � 1 3 " � � F " � < � V � � . 3 � $ � � � $ M 6 6 \� V � � . 3 � $ � � � $ � 3 5 � I � � $ 3 � : $ � 3 � " 5 3 ) & O \ V + " � � . 3 � $ � � � $ < 3 $ : � �

� � � . : . � I � 1 " � . . $ + � � : � I 5 � � $ � � � . ) 5 3 � � $ � 6 K � � I 6 3 � � $ � 3 . �

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Page 14: Simulation of Simultaneous Events in Regular Expressions

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Page 15: Simulation of Simultaneous Events in Regular Expressions

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õ Á É ½ Å Á Ú Á ¿ Å ½ ¼ Á Á Ä Í Ú Á Ç Á Á Ä Â ½ Ä Á ÷ Ç Á Â Ê Á Â Á Å ¾ Ë ò î ë è æ ì î ø æ í î ï ë Ì Ç Ä è ù ú î ó æ ò è ë û èï ð ò î ë è æ ì î ø æ í î ï ë Î

ü ý þ � � � ý � � � ý � þ î ë è æ ì î ø æ í î ï ë î ç æ í ï í æ ò ï ì � è ì ï ð æ ç è í ï ð è ó è ë í ç â � ð í å î ç ç è í û ï ë �ç î ç í ç ï ð è ó è ë í ç í å æ í å æ ó è ï û û ú ì è � ç î � ú ò í æ ë è ï ú ç ò � í å è ë í å è ï ì � è ì î ë � ï ð ç ú û åç î � ú ò í æ ë è ï ú ç è ó è ë í ç î ë í å è ç è í î ç ï ë è ò î ë è æ ì î ø æ í î ï ë ï ð í å î ç ç è í â ñ � î � è ì è ë í ï ì �

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+ Ð Å Æ Ç Õ Â Ê Æ Ë ¿ Ê Ì Ë Á Í Ú Á Ì Ä Ä Ì À Â Á Å Ç Ì Â Æ Ô Á Â Å Ì Ç Ë Æ Â Æ ½ Ç Ë Â ½ Ì ¿ ¿ Å ½ ¿ Å Æ Ì Â Á Ë Â Ì Â Á Ë Æ Ç, . 0 2 4 6 Î 8 Ê Á Ì À Â Á Å Ç Ì Â Æ Ô Á Â Å Ì Ç Ë Æ Â Æ ½ Ç Ë Â Ì Ý Á Â Ê Á + 9 : É Å ½ ¾ Ì Ë Â Ì Â Á Å Á ¿ Å Á Ë Á Ç Â ;

Æ Ç Õ ½ Ç Á À Æ Ç Á Ì Å Æ = Ì Â Æ ½ Ç Â ½ Ì Ç ½ Â Ê Á Å Ë Â Ì Â Á Å Á ¿ Å Á Ë Á Ç Â Æ Ç Õ Ì Ç Á ? Ð Æ Ô Ì À Á Ç Â À Æ Ç Á Ì Å Æ = Ì ;Â Æ ½ Ç É ½ Å Ë ½ ¾ Á Ë Á Â ½ É Ë Æ ¾ Ð À Â Ì Ç Á ½ Ð Ë Á Ô Á Ç Â Ë Î C Á Â E F H J L F O F R F T U Ò Á Ì Ç Á Ô Á Ç ÂË Â Å Æ Ç Õ ½ Ò Â Ì Æ Ç Á Ä Ò Ã Å Á ¾ ½ Ô Æ Ç Õ ½ Ç Á ½ ¼ ¼ Ð Å Å Á Ç ¼ Á ½ É F É Å ½ ¾ Ì Ç Á Ô Á Ç Â Ë Â Å Æ Ç Õ F T Î C Á ÂY [ T \ F _ O F T U Ò Á Ì Ê Ì Ë Ê Ô Ì À Ð Á Ì Ë Ë ½ ¼ Æ Ì Â Á Ä Ú Æ Â Ê Ì Ç Á Ô Á Ç Â Ë Â Å Æ Ç Õ F T Ú Ê Á Å Á Â Ê Á ½ Å ;Ä Á Å Æ Ç Õ ½ É Á Ô Á Ç Â Ë Æ Ç F T Æ Ë Æ Ç Ë Æ Õ Ç Æ ÷ ¼ Ì Ç Â Î 8 Ê Æ Ë ¾ Á Ì Ç Ë Â Ú ½ Á Ô Á Ç Â Ë Â Å Æ Ç Õ Ë Ê Ì Ô Á Â Ê ÁË Ì ¾ Á Ê Ì Ë Ê Ô Ì À Ð Á Æ É Ì Ç Ä ½ Ç À Ã Æ É Â Ê Á Ã Ì Å Á Á ? Ð Æ Ô Ì À Á Ç Â À Æ Ç Á Ì Å Æ = Ì Â Æ ½ Ç Ë Î 9 ½ Å Á Ø Ì ¾ ¿ À Á Í

e æ ç å è � O [ f g U h e æ ç å è � O g [ f U Ò Ð Â e æ ç å è � O [ [ f g U ih e æ ç å è � O [ f g U Îj k

Page 16: Simulation of Simultaneous Events in Regular Expressions

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� � � � � � � � ! # � % & � � ( * ! * � ! � - � . � % 1 � � � & # � � � 7 � * # & # � ! * � & � < # ( � & # � # � &# � & � � ( � � # � � � # � � B � � � C ! � � � � * # � ! * � � � ! � � # ! � * & � < # � � & � % � ! * 1 J # & � � J � * . � - < & � L ( � & � B # � � # # � � # ( � � 7 � * # & # � ! * � & � � � � � J ! 7 � � � * # � ! * � � � ! � � # ! � * & � < # � �! * 1 J # & � � J � * . � L � * C ( � . � J � C � C C � � # � � * � # ! 7 � # � � * & ! # ! � * & < � � % � * � & # � # � # �� * � # � � � ( ! # � � J # . � � * � ! * � # � � % � � * ! * � � < # � � � � � - � ! * . � ( � � � ( � B & . � � � & �� # � � * & ! # ! � * � < � � % � & # � # � � ( ! # � # � � � � ( � & # � � � � X � & # L # � � � � C � � � < 1 � # � &

# � Z � * ! & J * ! � J � - � � J & L ( � * � � C # � � C C � � # � � * � # ! 7 � # � � * & ! # ! � * & � * � B < � � % �& # � # � ( ! # � � � ( � � � � � � # � # � � & # � # � & ( ! # � � ! � � � � � � � � - � � ! & % � � * & # � � # ! < � � * C� b � � � & # � # � & L # � � * ( � � C C � � # � � * � # ! 7 � # � � * & ! # ! � * & < � � % � # � � b ! < � * C � * � B ! <

# � � % � d ! % J % 7 � � J � � < � � � b � � % � * � � � � # � � * & ! # ! � * & � b � < � b ! & � � � � # � � # � � * # � �% ! * ! % J % 7 � � J � � < � � � � � % � * � � � � # � � * & ! # ! � * & � � < � � � ! * � & ) + - � - / � � * � C C ! * �

# � � � � # � � * � # ! 7 � # � � * & ! # ! � * & � * * � # � # � C ( ! # � � * � 7 � * # 0 < � � % � # � � b L ( � � * & J � �# � � # # � � � d ! & # ! * � # � � * & ! # ! � * & ! * � C � * � # � � 7 � � # � � * & ! # ! � * � * * � # � # � C ( ! # � # � �� 7 � * # 0 � � ! * � 5 � - � � J & L # � � � � & J � # ! * � X * ! # � � J # � % � # � ! & & # ! � � C � # � � % ! * ! & # ! . -

� � � � � � � � # ( � C ! � � � � * # . � & � & ( � ! . � # � � � � � � � ! # � % � � * C � � & - � & & J % � 0 7 9: ; � � � � * C 0 7 b 9 : ; � � b � � � � # ( � � 7 � * # & # � ! * � & & J . � # � � # � � � & � � ( � � � � � � # � � *

� b - � � � X � & # . � & � ! & ( � � * & � % � � 7 � * # & # � ! * � & � < # � � # ( � & # � # � & � � * C � b � � 7 �C ! � � � � * # l J # � � J ! 7 � � � * # � ! * � � � ! � � # ! � * & - � � � � d � % 1 � � L 0 7 C D F H � * C 0 7 b C F H D -J � � � # � � � � � � � ! # � % � C C & � * � � # � � * � # ! 7 � # � � * & ! # ! � * � * # � � . J � � � * # � 7 � * # 0 < � � %

# � � & # � # � � # � # � � & # � # � � � 1 � � & � * # � C l B L � � b M 0 � � � ! * � & O + Q � - � � ! & # � � * & ! # ! � *! & � C C � C < � � � � . � � 7 � * # 0 & J . � # � � # # � � � � � � � * � # � � * & ! # ! � * & . J � � � * # � B 1 � � & � * #< � � % � � * � * B � < # � � & � � 7 � * # & - � � ! & . � & � ! & & � � ( * ! * � ! � - U V - J � � � L � C W L � b C Y L

0 7 C 0 [ 0 U 0 ) L 0 7 b C 0 U 0 [ 0 ) � * C 0 C 0 - - � � � � � � � � ! # � % # � � * � C C & � # � � * & ! # ! � * � *0 - # � L � Y M 0 - � ( � ! . � ! & # � � � . . � 1 # ! * � & # � # � � o -

� � � & � . � * C . � & � ! & ( � � * ` 0 a b c 0 � 0 M 0 7 b � � * C 0 7 � � 1 � � & � * # � � J ! 7 � � � * # � ! * d� � � ! � � # ! � * & < � � # � � # ( � & # � # � & � � * C � b - � � � � d � % 1 � � L ! < 0 7 C F D L 0 7 b C D 0 F L � * C

# � � . J � � � * # � 7 � * # ! & 0 L # � � * # � � � � % � 7 � � � < 0 < � � % 0 7 b � � # J � * & � * � 7 � * # & # � ! * �( � ! . � ! & � � J ! 7 � � � * # # � 0 7 - J � � � # � � � � � � � ! # � % � C C & � * � � # � � * � # ! 7 � # � � * & ! # ! � * � *# � � . J � � � * # � 7 � * # 0 < � � % � # � � b � � ! * � & � + U V � - � � � ! * # � � # � � * & ! # ! � * & � � � � C C � C� * � B < � � # � � & � � 7 � * # & # � � # . J � � � * # � B C � * � # � � 7 � # � � * & ! # ! � * & < � � % � - � � ! & . � & �! & & � � ( * ! * � ! � - U U - J � � � L � C W L � b C Y L 0 7 C 0 [ 0 U 0 ) L 0 7 b C 0 U 0 [ 0 5 0 ) � * C 0 C 0 5 -� � � � � � � � ! # � % # � � * � C C & � # � � * & ! # ! � * � * 0 5 # � Y -

� < # � � . � % 1 � � # ! � * � < # � ! & 1 � � & � L ( � . � * C � � � # � # � � � 7 � * # & # � ! * � ! * < � � % � # ! � *< � � % � � � # � � & # � # � & � d . � 1 # # � � � * � & ( ! # � k � � � 7 � � J � & � < U - / � . � � � # � � & �& # � # � & # � � 1 � * J � # ! % � # � & # � # � & - � � � ! � � 7 � * # & # � ! * � & ( ! � � l � J & � C # � 7 � � ! < B # � �� . . � 1 # � * . � � < # � � ! * 1 J # & � � J � * . � - � � ! & 1 � � . � & & ( ! � � l � � d 1 � � ! * � C ! * # � � * � d #& � . # ! � * -

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Page 17: Simulation of Simultaneous Events in Regular Expressions

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. 0 2 0 5 7 9 2 < = 7 9 ? . 7 9 7 9 2 D F ? 2 I 7 J K M N 0 � 2 R 7 5 ? 2 I . T V D = 7 2 X Z [ \ ] ^ _ F ` T = D D b 7 = � . _ c. _ 7 F d F _ I . f 2 ` = 7 . F _ 7 9 2 = D 7 2 ` _ = 7 . j 2 7 ` = _ I . 7 . F _ I = _ f J K M N 0

� 2 d = V I 2 2 j 2 _ 7 I 7 9 = 7 F d d V ` I . T V D 7 = _ 2 F V I D b d = _ = D I F F d d V ` . _ f . j . f V = D D b 5 I F T 2D . _ 2 = ` . ! = 7 . F _ 7 9 = 7 X Z [ \ ] ^ = d d 2 < 7 I T . c 9 7 _ F 7 u 2 = d d 2 < 7 2 f u b X Z [ " y ^ 0 { 9 2 _X Z [ \ ] ^ ` 2 = d 9 2 I 7 9 2 = d d 2 < 7 . _ c I 7 = 7 2 5 ? 2 j 2 ` . ~ b u b d F T < = ` . _ c 7 9 2 . _ < V 7 I 2 $

� V 2 _ d 2 = _ f 7 9 2 2 j 2 _ 7 I 7 ` . _ c I . _ 7 9 2 < 2 _ V D 7 . T = 7 2 I 7 = 7 2 I 7 9 = 7 9 = j 2 = _ F ` . c . _ = D7 ` = _ I . 7 . F _ F _ 7 9 2 D = I 7 2 j 2 _ 7 . _ 7 9 2 . _ < V 7 I 2 � V 2 _ d 2 7 F 7 9 2 = d d 2 < 7 . _ c I 7 = 7 2 0 � 2 $

d = V I 2 X Z [ " y ^ . I T . _ . T = D 5 F _ D b F _ 2 I V d 9 < 2 _ V D 7 . T = 7 2 I 7 = 7 2 2 R . I 7 I 0 � ~ 7 9 2 bT = 7 d 9 5 X Z [ \ ] ^ = d d 2 < 7 I 7 9 = 7 . _ < V 7 I 2 � V 2 _ d 2 0 ' 7 9 2 ` ? . I 2 5 X Z [ \ ] ^ ` 2 ) 2 d 7 I 0

� F u 2 = u D 2 7 F j 2 ` . ~ b 5 ? 2 _ 2 2 f 7 F � 2 2 < 7 9 2 9 . I 7 F ` b F ~ = D D 2 j 2 _ 7 I I 2 2 _ ~ ` F T7 9 2 I 7 = ` 7 I 7 = 7 2 0 � 9 2 9 . I 7 F ` b = D I F � 2 2 < I . _ ~ F ` T = 7 . F _ = u F V 7 ? 9 . d 9 2 j 2 _ 7 I 9 = j 2F d d V ` 2 f I . T V D 7 = _ 2 F V I D b = _ f ? 9 . d 9 9 = j 2 F d d V ` 2 f . _ f . j . f V = D D b 0 { 2 f F I F u bI 7 F ` . _ c 7 9 2 . _ < V 7 I 2 � V 2 _ d 2 = I = _ = ` ` = b F ~ I . T V D 7 = _ 2 F V I I 2 7 I 0 � F 9 = _ f D 2 - D 2 2 _ 2I 7 = ` 5 ? 2 9 = j 2 = / = c 7 F . _ f . d = 7 2 ? 9 2 7 9 2 ` F ` _ F 7 2 = d 9 I 7 = 7 2 9 = I u 2 2 _ j . I . 7 2 f 0{ 2 7 9 2 _ � 2 2 < F _ D b 2 j 2 _ 7 I 7 9 = 7 7 = � 2 7 9 2 I . T V D = 7 . F _ ~ ` F T F _ 2 I 7 = 7 2 7 F = _ F 7 9 2 `V _ j . I . 7 2 f I 7 = 7 2 0 � 9 . I ? = b 5 7 9 2 ` 2 I V D 7 . _ c 9 . I 7 F ` b I 7 ` . _ c ? . D D ` 2 I 2 T u D 2 7 9 2 ? = b2 j 2 _ 7 I 7 ` . _ c I = ` 2 d = D d V D = 7 2 f = _ f I . T < D . ~ b F V ` j 2 ` . 2 d = 7 . F _ = D c F ` . 7 9 T 0 � 2 7

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Page 18: Simulation of Simultaneous Events in Regular Expressions

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5 6 & " 9 ; = > ? A = ( * E G ? > �

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L 6 & " 9 ; = � = N P P S T V T W � X P V P G T W [

\ 2 � � T V = > � P �

^ 6 & " 9 � � � � �

_ ` N N = � P P S T V T W � X P V P G T W [ e T E T P S h V W ? P � = = W G = � = N P = k l

m T [ n � � n � = G T E � T W [ ` p [ ? G T P S >

� � � q s u v x y z x | v q ~ s � � � v u ~ � � ~ � � ~ � � � " � � $ q ~ � � u v ~ � ~ � v s � v q ~ s � � � v u ~ � � ~ � � ~ �& ( 0 � � � � � � u ~ v x | ~ � ~ � v u v y s � � u � u u x � s � v ~ � � s v q v q ~ � ~ � � � v s � � v ~ u v � v ~ � � q s � q

q � u � v y � � u s v s x � s � + - . 0 1 3 x � � � " � v x v q ~ � � � ~ � v s � � u v � v ~ � * � � u ~ v x | ~ � ~ � v u s � � � ~ � ~ � v u v y s � � � q ~ y ~ 5 s u v q ~ � x u s v s x � s � v q ~

~ � ~ � v u v y s � � �6 � � � u ~ v x | u s � � � v � � ~ x � u ~ � ~ � v u 6 � 8 � � q ~ y ~ 6 � x � � � y u � ~ | x y ~ 6 � : � �

$ q ~ � ~ y s | z s � � � � � x y s v q � s � ; s � � < = s u u v y � s � q v | x y � � y � � ; x y ~ � � q * 8 & ( 0 � � � �? � s � ~ = B � � ~ � q ~ � ¡ s | * x � � � y u s � v q ~ � � y y ~ � v u s � � � v � � ~ x � u u ~ v ? � s � ~ E B � F |

� x v � v q ~ s � � � v u v y s � � s u y ~ G ~ � v ~ � ? � s � ~ J B � L q ~ � v q ~ � � y y ~ � v u ~ v s u � x � N� � ~ v ~ � z � � y u ~ � � s v q x � v � ~ s � � y ~ G ~ � v ~ � � � ~ � x � ~ v x v q ~ � ~ ¨ v u ~ v ? � s � ~ u O Q S B �F | � ~ y ~ � � q v q ~ ~ � � x | & ( 0 � � � � � s v q x � v � ~ s � � y ~ G ~ � v ~ � � � ~ � � � ~ � v v q ~ s � � � vu ~ � � ~ � � ~ ? � s � ~ V B � ; x y ~ ¨ � � � � ~ � � ~ v v q ~ s � � � v u ~ � � ~ � � ~ y ~ � x y � ~ � � q ~ � v q ~W ; � � � � ~ � v ~ � � ~ Y < = [ ] [ _ a � q ~ y ~ ~ � ~ � v u < � � � = q � � ~ x � � � y ~ � u s � � � v � N

� ~ x � u � z � e s � � ~ v q ~ � � u v ~ � ~ � v s � v q ~ u ~ � � ~ � � ~ � s � ~ � � � � " � � _ � � ~ q � � ~ & ( 0 � � � �� Y < = ] [ < = E ] a � k x � u s � � ~ ~ � ~ � v u v y s � � Y < = ] a s � & ( 0 � � � � � � v � q ~ u

� s v q v q ~ y ~ � x y � ~ � s � � � v u ~ � � ~ � � ~ Y < = [ ] a � + - . � n 3 � s � � � � � ~ � v v q s u s � � � vu ~ � � ~ � � ~ �

­ ® p ¯ ° ± ² r ³ ´ ³ µ ¶ · ¸ ¹ ¯ ² t µ » ´ · ¸ u

$ q s u � � � � ~ � v � v s x � � � � x y s v q � q � u v q ~ | x � � x � s � � y � � � s � � v s � ~ u � � y s � � ~ � � q� q � u ~ � ; x y � q � u ~ < � � ~ y � � ¼ ; e v � s � ~ � � � � v q � u v q ~ y � � � s � � v s � ~ s u x ? y { } B

� q ~ y ~ y � � � � s u v q ~ � � � � ~ y x | u v � v ~ u � � � � } � � � � � ? � B � s u v q ~ � � � � ~ y x |v y � � u s v s x � u � ; x y � q � u ~ = � v q ~ y � � � s � � v s � ~ s u x ? y � � � y � B � q ~ y ~ � � � � s uv q ~ � � � � ~ y x | ~ � ~ � v u s � v q ~ y ~ � ~ � � � v u ~ v � � � y � � ¾ ¿ � � & ( ? � B � s u v q ~ � � � � ~ yx | � x u u s � � ~ ~ � ~ � v u v y s � � u s � v q ~ y ~ � � � � y ~ ¨ � y ~ u u s x � � ? � x y u v � � u ~ � � � � z u s u B � $ q s uv q ~ � � x � u v s v � v ~ u v q ~ � x � � s � ~ v s � ~ � ~ � � � v s ~ u | x y � � � � ~ � v s � � v q ~ W ; � � $ q ~

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Page 19: Simulation of Simultaneous Events in Regular Expressions

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� � � � � � � � ! # � � $ & ' ) � + � , � / � + 1 � ! � � ' � & 6 � / � , � � ! & + � � / ' 8 � � / � / � � � < �� � ! & + � � / ' & 6 > ? � ' � $ � � � ? , � ' 1 � � � � ! � � � ) & , , � � � � ) � � / , # � � $ � � / � + � $ � � �� � � � , 1 $ / ) � � / , 8 / � + � � � , � / � � � ! � / & 6 � / � � ) 1 � , � + � ! G � / � > ? � ' � $

, � ' 1 � � � � & � ) ) + & � $ / $ � � ' ) & , � � � > > � � � & � � + 1 � ! � � ' � & 6 � � � � # � & 1 +� � ! & + � � / ' G � � � � � > > � > � & � / � + 1 � ! � � ' � � , 6 & + < � + � U $ � � � & & 6 � / � � ) 1 �, � � 1 � $ � 8 / � � � � V � � $ $ � ) � , # " / � � > > � � � & � � , ) � $ � � , & � ? � � � & � � � $ � 1 , �

8 � � > > � � � � + � � � < � � + � , � � � & , & � ? 6 + & ' � & 8 � + 1 ' � � + � > � & / � ! / � + 1 ' � � + � >) � � / , G 8 / � $ / � , ) �\ ] ^ * , � � � & � # " / � + � 6 & + � G & 1 + � � ! & + � � / ' � , $ � � � + � ? ) + � 6 � + � >& < � + � / � � � < � � � ! & + � � / ' #

0 ` 2 a b c d e 3 4 6 f f c f 2 � c 3 g � � h i g

� 7 j k l m o p m l r s k t m v j v w k s s 8 k t x p � y { � | }

~ r � l � j t m j � � m t x k s t � � j k t m � � t � k j p m t m v j p � y � | � y � & |

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� � � � � � � � � � � � � � � � � � ; < � � ? � � � V �

� � / � , , � $ � � & G 8 � ) + & < � � � � ) + & & 6 � / � � � � � ; < � � � � � V � � + � � � 1 � < � � � � #

� � � B C � � � � � � � � V � � � � � D � � � � � � ? � � � F � � � � � ; < � � � � D � � �

� C B B � �� � ! " $ & ( * � � � ; < � , , / 1 " 4 6 � � � V � � , , / 1 " 4 ;

" / � , , � � � � ' � � $ � � � + � , � � � � � � , � 6 � � � ; < � $ $ � ) � , , & ' � � � � � + � K � � � & & 6� / � � ) 1 � , � � 1 � $ � G � / � � � � V � � $ $ � ) � , � � � & 6 � � , � � 1 � < � � � � � � � � + � K � � � & , #N � � � U � � ) � � / � � � , � � & 6 ) � � / , � , 6 & � � & 8 , # O ) � � / � � � � ; < � , � ? ) � � /6 + & ' � / � , � � + � , � � � � P ¢ � & � / � � $ $ � ) � � ! , � � � � P £ # ¥ < � + ? , 1 $ / ) � � / � , 1 � � 1 � � ?& + � � + � � � ? � / � � � ! & + � � / ' # O , � � & 6 ) � � / , � , � � 1 ' � + � � � & & 6 � � � ) & , , � � � �) � � / , 6 + & ' P ¢ � & P £ & 6 � � � ; < # ¨ ? � / � � � , $ + � ) � � & & 6 � / � � � ! & + � � / ' G � < � + ?� � � � + � � � < � � + � , � � � & � , � � + � , � � � & 6 + & ' & � ) � � / � & � & � / � + ) � � / � � / � , � � G� � � / � � + � , � � � & , � + � � � 8 � ? , � � ª � 6 + & ' � & 8 � + T � W � � & / � ! / � + T � W � #

Y � � Z � � � / � � < � � $ 1 + + � � � ? � � � ! $ & , � � � + � � # Y � � P ^ � � P & � � � / � � 8 &, � � � � , � � � ! $ & , � � � + � � # Y � � ] ^ ^ � � ] ^ & � � � / � � 8 & � < � � , � + � ! , � , , & $ � � � � �

8 � � / P ^ � � P & G + � , ) � $ � � < � � ? # O , , 1 ' � � / � $ 1 + + � � , � � � � � , P ^ G � � � / � + � 6 & + � G] ^ ^ � , & � � � � � + � K � � � & & 6 � ) 1 � , � � , & 6 � + # " / � � � ! & + � � / ' / � , � / � 6 & � � & 8 � !� � � � + � � � < � , #

� � � " / � � < � � , � + � ! ] ^ & � , � � � e � + � � � � 1 � < � � � � � � � � + � K � � � & & 6 � ) 1 � , � � , & 6 � + G � # � # G � f � � ° � ? � ] ^ ^ � , f � � ° � ? � ] ^ & � � # " / � G � / � � � ! & + � � / ' � � � ,� � � � � + � � � < � � + � , � � � & 6 + & ' P ^ � & � , � � � � P B & Z , 1 $ / � / � � � � + � j, � � � & 6 + & ' P & � & P B & Z � ± � , � , G � # � # G l � P & m Z � , P B # " / 1 , G � / � , � � j

� � + � � � < � � + � , � � � & � � ª � , � , � � ) 6 + & ' & � � � � � + � K � � � & � & � / � & � / � + #� f � � ° � ? � o p � o Z W � ] ^ ^ m Z � � , f � � ° � ? � o p � o Z W � ] ^ & m Z � � � #

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Page 20: Simulation of Simultaneous Events in Regular Expressions

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� � � � � � � � � � ! # % ' ! ) � ) � ! � � � � * % � � � � � � / 1 � 3 � # % ' � / 1 ' � / � % � � � % 1 � ! / ! ) 1 � �� / 8 3 1 * � � / * ! ) % � ; � � < = ? A � � � � B � � � < = ? A � � � � � � � � � � � � � � � ; � � � / E 1 � � *% ' G ! � � 1 � � % � � * % / % ' 1 � � / % 1 � # � 1 � % / * � 1 � ! / ) � ! � % B 1 ! % ! / � ; � � 3 * % G % � /

1 � � * % ' 1 � � / % 1 � # � 1 � % / * � 1 � ! / 1 % M � * % * 1 � 8 ) � ! � ! / � ' � / � % � � � % 1 � ! / 1 ! 1 � � ! 1 � � � ;� � < = ? A � � ( � * ( � , � � � B � � � � � < = ? A � � � � � � ;

/ ! V V � 8 � ! # � 1 � % 1 * 3 X � % ' 1 � � / % 1 � # � 1 � % / * � 1 � ! / * � [ � * 1 ) ! � � # � � ] 8 % � � ! ) � 3 � # 1% ' � / 1 ' � / � % � � � % 1 � ! / * ; 3 � 1 * 1 % 1 � * % B E % E % � E % � ^ � ' ! / G 1 ! 8 % 1 � * B E E � E � E

� � * 8 � X 1 � # � ' ] E % / � ' � 1 1 � � ! � � � � � / G ! ) 1 � � * � 8 % 1 � * ^ � B � � � � � ; � � � /1 � � ! � � � � � / G ! ) * 1 % 1 � * � * % B � % � % � � % � ; 9 ) ! / � ! ) 1 � � � # � / 1 * 1 � � / G * % * 1* ! X � % 1 � � V � 1 � � % X � ! ) 1 � � * � * 1 % 1 � * % � � � � � � � � / 1 � 3 � # % ' � / 1 ' � / � % � � � % 1 � ! / * % / �

1 � � ! � � � � � / G � * % * G � # � / % ^ ! # � E 1 � � / � 1 X % / ^ � * � � / 1 � % 1 1 � � % ' G ! � � 1 � � � � 8 � % 1 *� 1 * � ' ) ) ! � � % X � 8 % � � ! ) * 1 % 1 � * � % B % � � % B % � � � % B % � � � % % � � � % % � � % / � � % � % � �� / 1 � % 1 ! � � � � ; � � 3 * E 1 � � % ' G ! � � 1 � � 8 � ! # � � � * % 8 % 1 � 1 ! G ! ) � ! � 1 � � X 3 � � � / 1 ' � / 1� % � � � % 1 � ! / ! ) 1 � � � / 8 3 1 1 ! % / ] ! 1 � � � � � � � � � / 1 � 3 � # % ' � / 1 ' � / � % � � � % 1 � ! / G ! # � � / � �^ ] 1 � � 3 / � 3 � ! � � � � � / G ! ) ' � / � % � � � % 1 � ! / * � ! � 8 % 1 � * � ;

B � / X � % 1 � 3 / 1 � � � V � V � ' ' * � � 3 ' % 1 � C D E o G H ^ % * � � ! / 1 � � ! � � � � � / G ! ) 1 � �8 % 1 � * � ) � ! � % G � # � / 8 % 1 � ! ) I � , � � � E V � % ' V % ] * � % # � % 8 % 1 � 3 * � / G 1 � � % ' 11 � � / % 1 � # � 1 � % / * � 1 � ! / * 1 ! % ' ' 8 % 1 � * V � 1 � I � , � G � � % 1 � � 1 � % / � % / � � % # � / G * ! � �� 3 � # % ' � / 1 ' � / � % � � � % 1 � ! / ; � � 3 * E C D E o G H V � ' ' � # � / 1 3 % ' ' ] � � % X � 1 � � 8 % 1 � E V � � X �� � 8 � � * � / 1 * 1 � � ' � / � % � � � % 1 � ! / ) ! � V � � X � C D E N P H % X X � 8 1 * ; S / X � � 1 � � % X � � * 1 � � *8 % 1 � E 1 � � 8 � ! X � * * ! ) 8 � X M � / G ! � � G � / % ' 1 � % / * � 1 � ! / * s � * 1 � / * 3 � � * 1 � % 1 V � V � ' ' / � # � �' � % # � 1 � � * 8 % 1 � ;

� � � � ! # % ' C D E o G H � * * , - � / 1 C D E N P H � * * , - � / 6

U � 8 � ! # � 1 � � * X % * � ^ ] X ! / 1 � % � � X 1 � ! / ; V * * 3 � � 1 � % 1 C D E o G H % X X � 8 1 * % / �C D E N P H � ! � * / ! 1 ) ! � * ! � � � / 8 3 1 * � 3 � / X � ; t ] 1 � � � � s / � 1 � ! / ! ) 1 � � % ' G ! � � 1 � � EC D E o G H % X X � 8 1 * � ) 1 � � ) ! ' ' ! V � / G X ! / � � 1 � ! / * � [ � * 1 ;

� � � B � � 3 ' % 1 � ! / � � % X � � * 1 � � % X X � 8 1 � / G * 1 % 1 � ! ) C D E o G H ;

� � � � � � � � / 8 3 1 * � 3 � / X � ! / V � � X � C D E o G H � % * % X X � 8 1 � � � * � 3 � # % ' � / 1 1 ! 1 � �X ! / X % 1 � / % 1 � ! / ! ) % / � # � / 1 � v o W w % / � * ! � � � # � / 1 * 1 � � / G % * * ! X � % 1 � � V � 1 � 1 � �8 � / 3 ' 1 � � % 1 � * 1 % 1 � V � � X � � % * % 1 � % / * � 1 � ! / ! / % / � # � / 1 � v o W w 1 ! 1 � � % X X � 8 1 � / G* 1 % 1 � E V � � � � � v o W w � * 1 � � ' % * 1 � # � / 1 1 � % 1 ! X X 3 � * � / 1 � � � / 8 3 1 * � 3 � / X � ;

X � ! � 1 � � � � s / � 1 � ! / ! ) � # � / 1 * 1 � � / G * % 1 % * 1 % 1 � E V � X % / X ' % � � 1 � % 1 1 � � � # � / 1* 1 � � / G * 1 ! � � � % 1 1 � � 8 � / 3 ' 1 � � % 1 � * 1 % 1 � � * � 3 % ' 1 ! % * 1 � � / G 8 % � * � � ^ ] C D E N P H 1 !� � % X � 1 � � * * 1 % 1 � ; � � � * X ' % � � � * # % ' � � ^ � X % 3 * � V � � ' � � � 1 � � � � / � / G � # � / 1 * 1 � � / G * EV � 3 * � ! / ' ] 1 � � ! � � G � / % ' 1 � % / * � 1 � ! / * 8 � � * � / 1 � / C D E N P H ; � � � 1 � % / * � 1 � ! / 1 % M � /) � ! � 1 � � 8 � / 3 ' 1 � � % 1 � * 1 % 1 � 1 ! � � % X � 1 � � % X X � 8 1 � / G * 1 % 1 � � * % ' * ! % / ! � � G � / % '1 � % / * � 1 � ! / ; � � � � � ) ! � � E 1 � � � # � / 1 * 1 � � / G X ! / X % 1 � / % 1 � � ^ ] 1 � � ' % * 1 1 � % / * � 1 � ! / � *% X X � 8 1 � � ^ ] C D E N P H E X ! / 1 � % � � X 1 � / G 1 � � % * * 3 � 8 1 � ! / % ^ ! # � ; ;

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Page 21: Simulation of Simultaneous Events in Regular Expressions

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� � � � � � � � � � �

� � � � � � � � � � � " � % & ( ) & + , " / � 0 ( ) � � ) & + 5 / � 6 / � � ) � � � , 9 : � � � % 6 � � ( ( & / + ( & + ) / : / , & 5 ?� � � � / � � 6 � 5 � � B 6 / � � : � / , & 5 � � � � � � � � D + ) � : � ( + � " � / � B � : ( 6 � 5 & I 5 � ) & / + : � + �, 9 � , � D � % ) � + � ( � : & + � � � ) � B 6 / � � : : / , & 5 � � � � " & ) � ) � � � R & : & ) S ) / ( 6 � 5 & � S � : : � �� � , 9 : � � 6 � / 6 � � ) & � ( ? � � � � : : / " ( � 9 ( � � ) / � � I + � ) � B 6 / � � : 5 / + + � 5 ) & \ � ( / \ � � ) & B �" & + � / " ( D � � , 9 : � � ( � � 9 � + 5 � ( / � ^ / / : � � + � \ � + ) ( D � + � ) � � + � � : � ) � ( 9 5 � � \ � + ) ( \ & �( 6 � 5 & � : 5 / + + � 5 ) & \ � ( ? � 9 , � � � � � � � � ( � + � % ) � + ( & \ � ( � ) / � / 6 � � � ) / � ( & + 5 : 9 � & + ,� � , 9 : � � � % 6 � � ( ( & / + ( � ( � f � g h j k h m k f o � j p ) / r � � � � � ? " � / 6 � � ) S � 6 � 5 & I 5 � ) & / +� � + , 9 � , � � � � & ( � ( 6 � 5 & I 5 � ) & / + : � + , 9 � , � � / � � � � � " � � � B / � � : & + , � + � \ � � & I 5 � �

) & / + D " � & 5 � ( 9 6 6 / � ) ( � � � � � � � � + � � % ) � + � � � � � , 9 : � � � % 6 � � ( ( & / + ( ? ( / + & ) / � & + ,/ � & � + ) � � " � / , � � B B & + , � ( / " � � � 6 � / \ & � � ( � B / + & ) / � & + , � � 5 � & ) � 5 ) 9 � � R � ( � �/ + � � � � � � � � + � � % ) � + � � � � � , 9 : � � � % 6 � � ( ( & / + ( ? � � B 6 / � � : / / \ � � � $ � & ( � + � � �5 � & ) � 5 ) 9 � � ) � � ) � � : 6 ( � ( S ( ) � B � / B / + & ) / � & + , ? ) ( ( 6 � 5 & I 5 � ) & / + : � + , 9 � , � 9 ( � (� � � � � � � � + � ( � � � � ( � " & ) � � � , 9 : � � � % 6 � � ( ( & / + ( � + � � & B � � � � � & � ( ? � & B � � � � � & � (/ R ( � � \ � ( ) � B 6 / � � : 6 � / 6 � � ) & � ( / \ � � ) & B � � + � & ( 9 ( � � � / � 6 � / 6 � � ) & � ( : & 0 � ( ) � R & : �& ) S D B / + / ) / + & 5 & ) S D ) � B 6 / � � : � \ � � � , � D ( 9 B D � + � B � % 5 B & + \ � : 9 � ? r / B 6 � � & + ,) / ) � � ( { , � � / { R � ( � � / + � � � � + � � � , 9 : � � � % 6 � � ( ( & / + ( D � � � � � � D ( / " � � D

� + � � � B 6 / � � : / / \ � � � $ � 6 � / \ & � � ( & B & : � � : � + , 9 � , � ( R � ( � � / + � � � � + � 5 / � ( � �� + � � � , 9 : � � � % 6 � � ( ( & / + ( " � & : � � 9 , � � � � � � ( : � + , 9 � , � & ( R � ( � � / + r � � � + � ( & B �& : � � � � , 9 : � � � % 6 � � ( ( & / + ( ? 0 / " � \ � � D + / + � / � ) � � B ( � � B ) / � � \ � ) � � & ( ( 9 � / �( & B 9 : ) � + � / 9 ( � \ � + ) ( � + � ) � � � � � / � � + / � : , / � & ) � B � / � 5 � � 5 0 & + , � � 6 � + � � + 5 S � + �� 9 , B � + ) & + , � , � 1 � � ( R � � + 6 � / 6 / ( � � ?

= > � ? A � D E F � ?

2 � � � \ � 6 � � ( � + ) � � � + � : , / � & ) � B ) / ( & B 9 : � ) � � + � 9 , B � + ) � � , � 1 � / � ) � � � % �) � + ( & / + ( { , � � / { ? � � � ( { , � � / { & + 5 / � 6 / � � ) � ( � � , 9 : � � � % 6 � � ( ( & / + ( D " � & 5 �6 � / \ & � � � B / � � & + ) 9 & ) & \ � � + � : � ( ( � � � / � � 6 � / + � : � + , 9 � , � ) / � % 6 � � ( ( 5 / B 6 : � % � � �6 � + � � + 5 & � ( R � ) " � � + ( � � 9 � + 5 � / � � \ � + ) ( D ) & B & + , 5 / + ( ) � � & + ) ( D � + � � � � � � 9 � + 5 S / �� \ � + ) ( � 9 � & + , � ) & B � & + ) � � \ � : ? � � � � \ � + ) ( � ( ( / 5 & � ) � � " & ) � � � � , 9 : � � � % 6 � � ( ( & / +/ 5 � � ( ) � � � R & : & ) S ) / � � ) � 5 ) ) � � & + ( ) � + 5 � " � � + ) � � � � , 9 : � � � % 6 � � ( ( & / + ( ) � � ) ( � + �

) � � & + ( ) � + 5 � " � � + " � ( 9 5 5 � � � / � � � & : ) / I + � ) � � � � , 9 : � � � % 6 � � ( ( & / + ? � � � , � 1& ( � 9 , B � + ) � � R S � � � & + , � : ) � � + � ) & \ � ) � � + ( & ) & / + ( � � ) � � " � ( ) � ) & 5 � : : S � � ) � 5 ) ) � �6 / ( ( & R & : & ) S / � ( & B 9 : ) � + � / 9 ( � \ � + ) ( ? 2 � � : ( / 6 � / \ � ) � � ) ) � � � 9 , B � + ) � � , � 1 & (� � 9 & \ � : � + ) ) / ) � � / � & , & + � : , � 1 ?

� � J � � � ? A � E

M } N ~ � � � � � � � � P � � � � � R � � � � � S T � � � U V X Y � V [ ] _ Y � a c d a � [ c X g i � g j k � j � m � n � V � g a �o � g k � q s t � V � c X g v x y v S � � � � � z { { } � � � � � � � � � � � � � � � � � � � � � �

M � N ~ � 8 � ~ � � S � � � � � � � S � � � � � � � � � � � � � � � X � Y c q � V � � U V c g a c Y q � � s � � a � g c � k � � s � g �� X X q � � ~ � � � � � � � � � � � � : S � � � � � � � S � ~ S } � � � �

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Page 22: Simulation of Simultaneous Events in Regular Expressions

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� � � � � � � � � � � � � � ! � � � � � ! # % � ' ) * � � � � � * � / ) � � � � � � ' � 2 � 3 � � � � % � � % � � � � % � 6 7 * � �� � � % 6 � � � � % � � � � � � � � 3 * � � % � � � � � � * � * � * � � � � ! � � % � 6 � � % � 6 ! � # � % � � � ) *

! � � ' � * D � * � � � � % # � � 3 � D ( � * * , � * � � � � % # . � � � * � / � � � � * D � 2 D % / � � � � % � 3 2 % 3 * �4 � 6 7 7 8 I J : K < 8 > 7 ? A C M D I F 7 ? H 7 : I C ? L M C A 7 : J : K < : J 8 P I A I 7 F T P I C Q D I � � % 3 * ' R S T U

R U U � R V V R �

� X � 4 � � * * � � � � � * � � X % 7 � 6 � Z � � � ' � * � � X � ! � ' � % � � � � � � � � 3 % 2 � * � % � 6 ! � � � 6 * ) �� ) * � * � � � � % # � � 3 � D � 2 3 % � � _ Q M C L ? Q ` 7 C Q I A : H 7 D d L C Q ? T M A Q : M Q � R U V R ( � T � U � T _ �R V V U �

� ` � g � � � � � � � � � , ' h � � X * � � 7 % / � 7 * ' � b � * 3 2 # % � � � � � * ' ' � � � ' � j 7 L ? : J 8 7 F C M Q < H l �U U c X d ( X e U U X S X � U S T X �

� T � ! � Z ) * � % � 6 � � � � ' 2 � � � , % � 6 ' � � � � / � � � � 3 � p � � * � / * 6 . � � 3 � % � � � � 3 ( �. % � % 6 � 3 � Z � � � � � � � 3 � � * D � 2 D % / � � � % � 6 4 � � # * � * � / % / � � � � 4 � u ? 7 M Q Q K A : > I 7 F C M Q

w : K y : C Q ? : J C A 7 : J 8 z 7 ? | I M 7 d 7 : ~ L : � C A D Q � Q ? A � M J C A 7 : � g 2 # � R V V � �

� _ � � � � � Z # % � h * % � 6 � � � � � � * � ' � � � � � � / ) * ' � ' � b � � � D ) � � � � � % / � � � � h * # * / � � ' b � �� � % � D ) � � 3 � � � * � * � � � � % # � � 3 � D � 4 � _ 7 > A M 7 F u ? 7 > ? J D I � z 7 ? | I M 7 d _ Q M C L ? Q

` 7 C Q I A : H 7 D d L C Q ? T M A Q : M Q � 7 8 � w � � � Q � C Q ? J : K � 7 � Q : � Q K A C 7 ? I � � ! � � h / � , �� * � 3 ) / ' � * * , ! � � h � U S e U � � � � � � 3 * � � � * � # % 3 �

� e � X � X � 2 ' � � ' h � � � � � � / � � � � 3 � * � � � � % # � 2 # * ' Z � � � � � * 6 , � / ) � � � * � * � � * ' � 4 �u ? 7 M Q Q K A : > I 7 F C M Q � � � w H 7 D d L C Q ? < A K Q K � Q ? A � M J C A 7 : H 7 : F Q ? Q : M Q � H < � � � g 2 # �R V V � �

� S � � � � � � � y : F 7 ? D J C A 7 :   � C ? J M C A 7 : F 7 ? ~ L : � C A D Q � 7 ? D J 8 < : J 8 P I A I � . ) X / ) * ' � ' �¡ � � 7 * � ' � / � � b . * � � ' � # 7 % � � % � R V V U �

� U V � � � � � � � 4 � � * * � ¡ � � % � � % � 2 � � g � � ) � � � % � 6 p � � � h � # ' h � � � � � � / � � � � 3 � Z ) * D h � � 3 �% � 6 � / * * � � � 3 � b � * % # � � � � * � � ' / * � ' � 4 � u ? 7 M Q Q K A : > I 7 F C M Q � : K y : C Q ? : J C A 7 : J 8

z 7 ? | I M 7 d 7 : ~ L : � C A D Q � Q ? A � M J C A 7 : � g 2 # � R V V R �

� U U � � � � � � � � � � � ' , % � % / ) % � � � � � � � % � �* � * � * � � � � 6 % # # % ) � 4 � � * * � % � 6 p � � � h � # ' h � �! � � � % # # � � � * D � 2 * 6 � � � � / � � � � 3 � b � * � � � � % # . � � � * � / � * ' � 4 � u ? 7 M Q Q K A : > I 7 F C M Q  L ? 7 d Q J : H 7 : F Q ? Q : M Q 7 : ~ Q J 8 � 6 A D Q T P I C Q D I �   H ~ 6 T � � � � � % 3 * ' U U X U U R U � g 2 � *

U S S S �

� U R � � � � � � � % � ' � � � * D � b � � � 3 � * % # � � � � * . � � � * � / � * ' , � / ) � * / � � D � * � � � � % # � � 3 � D �~ Q J 8 6 A D Q T P I C Q D I � R c X d ( R ` ` U R S S � U S S V �

� U � � # � � % � � % % � 6 � � . � 2 * # � � 6 M Q 6 Q D d 7 ? J 8 _ 7 > A M 7 F ~ Q J M C A Q J : K H 7 : M L ? ? Q : CT P I C Q D I � � � � � � 3 * � � � * � # % 3 � U S S R �

� U X � ¡ � � % � � % � 2 � % � 6 p � � � h � # ' h � � � * 3 2 # % � � � � � * ' ' � � � ' b � � � 2 � � � � � * � * � � 2 D % / � � � �4 � u ? 7 M Q Q K A : > I 7 F C M Q � I C y : C Q ? : J C A 7 : J 8 z 7 ? | I M 7 d 7 : < L C 7 D J C Q K 6 Q M M : 7 8 7 > P F 7 ?

� Q ? A � M J C A 7 : J : K < : J 8 P I A I � X * D � R V V � �

� U ` � � � ¦ � ¦ % / ' � � � 6 J � 7 : 7 D A Q I J : K 6 7 7 8 | A C I 7 F ~ Q > L 8 J ? _ J : > L J > Q I < 8 > 7 ? A C M D I �. ) X / ) * ' � ' � � � � 6 ) � 7 * � ¡ � � 7 * � ' � / � � b � * D ) � � # � 3 � � U S S ` �

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