buchi automata
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Buchi Automata . Presentation. History . Julius Richard Büchi (1924–1984) Swiss logician and mathematician. He received his Dr. sc. nat. in 1950 at the ETH Zürich Purdue University, Lafayette, Indiana had a major influence on the development of Theoretical Computer Science. - PowerPoint PPT PresentationTRANSCRIPT
Buchi Automata Presentation
Julius Richard Büchi (1924–1984) Swiss logician and mathematician. He received his Dr. sc. nat. in 1950 at the
ETH Zürich Purdue University, Lafayette, Indiana had a major influence on the development
of Theoretical Computer Science.
History
Infinite words accepted by finite-state automata. The theory of automata on infinite words
more complex. non-deterministic automata over infinite inputs
more powerful. Every language we consider either consists
exclusively of finite words or exclusively of infinite words.
The set ∑ω denotes the set of infinite words
What is Buchi Automata ?
Many Systems including: Operating system Air traffic control system A factory process control system
What is common about these systems? such systems never halt. They should accept an infinite string of
inputs and continue to function.
Where it is used?
The formal definition of Buchi automata is (K, ∑, Δ, S,A).
K is finite set of states ∑ is the input of alphabet Δ is the transition relation it is finite set of:
(K * ∑) * K. S ⊆ K is the set of starting states. A ⊆ K is the set of accepting states. Note: could have more than start state & ε-
transition is not allowed.
Formal defination
Buchi (K, ∑, Δ, S,A). K is finite set of states ∑ is the input of alphabet Δ is the transition relation it is finite subset of: (K * ∑) * K. S ⊆ K is the set of starting states. A ⊆ K is the set of accepting states.
DFSM (K, ∑, δ, S,A). K is finite set of states ∑ is the input alphabet δ is the transition Function. it maps from: K * ∑ to K. S ϵ K is the start state. A ⊆ K is the set of accepting states.
DFSM Vs Buchi
Suppose there are six events that can occur in a system that we wish to model. So let ∑ = {a, b, c, d, e, f} in that case let us consider an event that f has to occur at least once, the Buchi automation accepts all and only the elements that Σω that contains at least one occurrence of f.
Example 1
Example 2This is example where e occurs ones.
Example 3This is an where c occurrence at least three
times.
Let L ={ w ϵ {0, 1}ω): #1(w) is finite } Note that every string in L must contain an infinite number of 0’s.
The following nondeterministic Buchi automaton accepts L:
Conversion From Deterministic to Nondeterministic
Thank You
?
1. Rich, Elaine. Automata, Computability and Complexity Theory and Applications. Upper Saddle River (N. J.) Pearson Prentice Hall, 2008. Print.
2. http://www.math.uiuc.edu/~eid1/ba.pdf
3. Http://www.cmi.ac.in/~madhavan/papers/pdf/tcs-96-2.pdf. Web.
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