engineering of chemical register...
TRANSCRIPT
Outline Motivation Register Machines Chemical Implementation Case Study Future Work
Engineering of Chemical Register MachinesPrague International Workshop on Membrane Computing 2008
R. Fassler, T. Hinze, T. Lenser and P. Dittrich{raf,hinze,thlenser,dittrich}@minet.uni-jena.de
2. June 2008
Ra�ael Fassler Engineering of Chemical Register Machines
Outline Motivation Register Machines Chemical Implementation Case Study Future Work
Outline
1 MotivationGoalRealizationP-System
2 Register Machines
3 Chemical ImplementationChemical VariablesA Chemical ClockMaster Slave - Flip�opChemical RegistersChemical Program Control
4 Case StudyInteger AdditionMaximum
5 Future Work
Ra�ael Fassler Engineering of Chemical Register Machines
Outline Motivation Register Machines Chemical Implementation Case Study Future Work
Motivation
Goal: Chemical system with Turing completenessUse mass action kinetics onlyBinary chemical information encodingNo assumptions like molecule structureor a hierarchy of membranes
Ra�ael Fassler Engineering of Chemical Register Machines
Outline Motivation Register Machines Chemical Implementation Case Study Future Work
Motivation
Realization: Arti�cial chemistry as P-SystemRegisters composed of �ip �ops store informationChemical clock orders operations on registersP-System expands registers if necessary
Ra�ael Fassler Engineering of Chemical Register Machines
Outline Motivation Register Machines Chemical Implementation Case Study Future Work
P-Systems as Arti�cial Chemistries
Similarities:
Many autonomous units like molecules or agentsDecentralizationNondeterminismStochasticityData parallelism
Ra�ael Fassler Engineering of Chemical Register Machines
Outline Motivation Register Machines Chemical Implementation Case Study Future Work
Register Machine
De�nition: M = (R,L, P,#0) withRegisters R = {R1, . . . ,Rm}Labels (addresses) L = {#0, . . . ,#n}Instructions PInitial label #0
Registers store binary values for natural numbers
Ra�ael Fassler Engineering of Chemical Register Machines
Outline Motivation Register Machines Chemical Implementation Case Study Future Work
1 MotivationGoalRealizationP-System
2 Register Machines
3 Chemical ImplementationChemical VariablesA Chemical ClockMaster Slave - Flip�opChemical RegistersChemical Program Control
4 Case StudyInteger AdditionMaximum
5 Future Work
Ra�ael Fassler Engineering of Chemical Register Machines
Outline Motivation Register Machines Chemical Implementation Case Study Future Work
Mass Action Kinetics
De�nition: Speed of an reaction depends on reactantsconcentrations and a constant factorNo saturationNo inhibitors
Ra�ael Fassler Engineering of Chemical Register Machines
Outline Motivation Register Machines Chemical Implementation Case Study Future Work
Chemical Implementation of Logical Variables
Variables: Two species representing "true" and "false"Correlated concentrationsReactions to switch between "true" and "false"Reactions to maintain consistency
Ra�ael Fassler Engineering of Chemical Register Machines
Outline Motivation Register Machines Chemical Implementation Case Study Future Work
A Chemical Clock
Based on Belousov- Zhabotinsky reactions
Cascade of variables derives high/low signals
Two o�set oscillators form the clock signal
Ra�ael Fassler Engineering of Chemical Register Machines
Outline Motivation Register Machines Chemical Implementation Case Study Future Work
Master Slave - Flip�op (MS-FF)
MS-FF: - technical role model
Two-part device storing one bitClocked to switch with o�setShort switches at intended timeOnly one switch per positive edge
Ra�ael Fassler Engineering of Chemical Register Machines
Outline Motivation Register Machines Chemical Implementation Case Study Future Work
Master Slave - Flip�op
MS-FF: - chemical adaption
Master part switches if triggeredSlave part will adapt master partEncoded by two variablesM/S-reactions separated by two clock signals
Ra�ael Fassler Engineering of Chemical Register Machines
Outline Motivation Register Machines Chemical Implementation Case Study Future Work
Master Slave - Flip�op
MS-FF: - chemical adaption
Master part switches if triggeredSlave part will adapt master partEncoded by two variablesM/S-reactions separated by two clock signals
Ra�ael Fassler Engineering of Chemical Register Machines
Outline Motivation Register Machines Chemical Implementation Case Study Future Work
Master Slave - Flip�op
MS-FF: - chemical adaption
Master part switches if triggeredSlave part will adapt master partEncoded by two variablesM/S-reactions separated by two clock signals
Ra�ael Fassler Engineering of Chemical Register Machines
Outline Motivation Register Machines Chemical Implementation Case Study Future Work
Master Slave - Flip�op
MS-FF: - chemical adaption
Master part switches if triggeredSlave part will adapt master partEncoded by two variablesM/S-reactions separated by two clock signals
Ra�ael Fassler Engineering of Chemical Register Machines
Outline Motivation Register Machines Chemical Implementation Case Study Future Work
Chemical Registers
Registers: One MS-FF for each bit, chainedExtra variable to check if emptyOnly the �rst bit can be �ipped manuallyAdd carries will �ip further bits
Ra�ael Fassler Engineering of Chemical Register Machines
Outline Motivation Register Machines Chemical Implementation Case Study Future Work
Chemical Registers
Registers: One MS-FF for each bit, chainedExtra variable to check if emptyOnly the �rst bit can be �ipped manuallyAdd carries will �ip further bits
Ra�ael Fassler Engineering of Chemical Register Machines
Outline Motivation Register Machines Chemical Implementation Case Study Future Work
Chemical Registers
Registers: One MS-FF for each bit, chainedExtra variable to check if emptyOnly the �rst bit can be �ipped manuallyAdd carries will �ip further bits
Ra�ael Fassler Engineering of Chemical Register Machines
Outline Motivation Register Machines Chemical Implementation Case Study Future Work
Chemical Registers
Registers: One MS-FF for each bit, chainedExtra variable to check if emptyOnly the �rst bit can be �ipped manuallyAdd carries will �ip further bits
Ra�ael Fassler Engineering of Chemical Register Machines
Outline Motivation Register Machines Chemical Implementation Case Study Future Work
Chemical Registers
Registers: One MS-FF for each bit, chainedExtra variable to check if emptyOnly the �rst bit can be �ipped manuallyAdd carries will �ip further bits
Ra�ael Fassler Engineering of Chemical Register Machines
Outline Motivation Register Machines Chemical Implementation Case Study Future Work
Chemical Registers
Registers: One MS-FF for each bit, chainedExtra variable to check if emptyOnly the �rst bit can be �ipped manuallyAdd carries will �ip further bits
Ra�ael Fassler Engineering of Chemical Register Machines
Outline Motivation Register Machines Chemical Implementation Case Study Future Work
Chemical Registers
Registers: One MS-FF for each bit, chainedExtra variable to check if emptyOnly the �rst bit can be �ipped manuallyAdd carries will �ip further bits
Ra�ael Fassler Engineering of Chemical Register Machines
Outline Motivation Register Machines Chemical Implementation Case Study Future Work
Chemical Program Control
3 Elements per Instruction: #1 : DEC R1 #0
Address - reaction that produces instruction speciesAction - reaction that alters/tests register
Follow up - species encoding the next label
Ra�ael Fassler Engineering of Chemical Register Machines
Outline Motivation Register Machines Chemical Implementation Case Study Future Work
Chemical Program Control
3 Elements per Instruction: #1 : DEC R1 #0
Address - reaction that produces instruction speciesAction - reaction that alters/tests register
Follow up - species encoding the next label
Ra�ael Fassler Engineering of Chemical Register Machines
Outline Motivation Register Machines Chemical Implementation Case Study Future Work
Chemical Program Control
3 Elements per Instruction: #1 : DEC R1 #0
Address - reaction that produces instruction speciesAction - reaction that alters/tests register
Follow up - species encoding the next label
Ra�ael Fassler Engineering of Chemical Register Machines
Outline Motivation Register Machines Chemical Implementation Case Study Future Work
Chemical Program Control
3 Elements per Instruction: #1 : DEC R1 #0
Address - reaction that produces instruction speciesAction - reaction that alters/tests register
Follow up - species encoding the next label
Ra�ael Fassler Engineering of Chemical Register Machines
Outline Motivation Register Machines Chemical Implementation Case Study Future Work
Chemical Program Control
3 Elements per Instruction: #1 : DEC R1 #0
Address - reaction that produces instruction speciesAction - reaction that alters/tests register
Follow up - species encoding the next label
Ra�ael Fassler Engineering of Chemical Register Machines
Outline Motivation Register Machines Chemical Implementation Case Study Future Work
Chemical Program Control
3 Elements per Instruction: #1 : DEC R1 #0
Address - reaction that produces instruction speciesAction - reaction that alters/tests register
Follow up - species encoding the next label
Ra�ael Fassler Engineering of Chemical Register Machines
Outline Motivation Register Machines Chemical Implementation Case Study Future Work
Chemical Program Control
3 Elements per Instruction: #1 : DEC R1 #0
Address - reaction that produces instruction speciesAction - reaction that alters/tests register
Follow up - species encoding the next label
Ra�ael Fassler Engineering of Chemical Register Machines
Outline Motivation Register Machines Chemical Implementation Case Study Future Work
Chemical Program Control
3 Elements per Instruction: #1 : DEC R1 #0
Address - reaction that produces instruction speciesAction - reaction that alters/tests register
Follow up - species encoding the next label
Ra�ael Fassler Engineering of Chemical Register Machines
Outline Motivation Register Machines Chemical Implementation Case Study Future Work
Chemical Program Control
3 Elements per Instruction: #1 : DEC R1 #0
Address - reaction that produces instruction speciesAction - reaction that alters/tests register
Follow up - species encoding the next label
Ra�ael Fassler Engineering of Chemical Register Machines
Outline Motivation Register Machines Chemical Implementation Case Study Future Work
Case Study
Implemented Examples:
Counter mod 4Integer additionMax(x,y,z)
Ra�ael Fassler Engineering of Chemical Register Machines
Outline Motivation Register Machines Chemical Implementation Case Study Future Work
Case Study
Integer Addition: 2 + 1 = 3
Ra�ael Fassler Engineering of Chemical Register Machines
Outline Motivation Register Machines Chemical Implementation Case Study Future Work
Integer Addition
Initialization: 2 + 1 = 3
Ra�ael Fassler Engineering of Chemical Register Machines
Outline Motivation Register Machines Chemical Implementation Case Study Future Work
Integer Addition
Computation: 2 + 1 = 3
Ra�ael Fassler Engineering of Chemical Register Machines
Outline Motivation Register Machines Chemical Implementation Case Study Future Work
Maximum of Three Natural Numbers
Computation: max(2, 1, 3)
Ra�ael Fassler Engineering of Chemical Register Machines
Outline Motivation Register Machines Chemical Implementation Case Study Future Work
Maximum of Three Natural Numbers
Computation: max(2, 1, 3)
Ra�ael Fassler Engineering of Chemical Register Machines
Outline Motivation Register Machines Chemical Implementation Case Study Future Work
Maximum of Three Natural Numbers
Computation: max(2, 1, 3)
Ra�ael Fassler Engineering of Chemical Register Machines
Outline Motivation Register Machines Chemical Implementation Case Study Future Work
Maximum of Three Natural Numbers
Computation: max(2, 1, 3)
Ra�ael Fassler Engineering of Chemical Register Machines
Outline Motivation Register Machines Chemical Implementation Case Study Future Work
Maximum of Three Natural Numbers
Computation: max(2, 1, 3)
Ra�ael Fassler Engineering of Chemical Register Machines
Outline Motivation Register Machines Chemical Implementation Case Study Future Work
Future Work
Parallelization:
Consecutive read/write operations are mergedinto threadsOperations in an thread are performed parallelThreads take the same time as a single operation
Ra�ael Fassler Engineering of Chemical Register Machines
Outline Motivation Register Machines Chemical Implementation Case Study Future Work
Thank you for your attention!
Ra�ael Fassler Engineering of Chemical Register Machines