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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 Presentation

Text of Buchi Automata

Butchi AutomataSwiss 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
The theory of automata on infinite words
more complex.
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 ?
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
∑ 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).
∑ is the input alphabet
δ is the transition Function. it maps from: K * ∑ to K.
S 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 2
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This is an where c occurrence at least three times.
Let L ={ w {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
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