automata-2 - Automata Ch2FiniteAutomata Simpleautomata...

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Automata Chapter 2 Finite Automata
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Ch 2 Finite Automata Simple automata: No temporary storage Limited memory  Only by finite states                        in  the control
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2.1 Deterministic Finite Accepters Def 2.1: A DFA is defined by  M=(Q, Σ , δ ,q 0 ,F), where Q is a finite set of  internal states , Σ  is a finite set of symbols called the  input  alphabet , δ : Q X  Σ    Q is a total function called the  transition function , q 0 Q is the  initial state ,  Q is a set of  final states .
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2.1 Deterministic Finite Accepters A DFA : M=(Q, Σ , δ ,q 0 ,F)                                         δ (q i,  a) = q j Transition Graph: |Q| vertices  q 0 : initial vertex, q  F: final vertices Input tape : left   right q i q j a
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2.1 Deterministic Finite Accepters Ex 2.1      M = ({ q 0  , q 1 , q 2 }, {0,1},  δ , q 0 , {q 1 })              δ (q 0 ,0) = q 0                     ……. q 0 q 2 q 1 0 0 0 1 1 1
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2.1 Deterministic Finite Accepters Extended transition function  δ *: Q X  Σ  Q   δ *(q, λ ) = q,    δ *(q, wa) =  δ ( δ *(q,w),a)   for all q Q, w ∈Σ *, a ∈Σ δ (q 0,  a) = q δ (q 1,  b) = q   δ *(q 0,  ab) = q 2 Try  δ *(q 0,  ab) = q 2  with the above def. Given w, if  δ *(q 0,  w)   F then w is accepted.
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2.1 Deterministic Finite Accepters Def 2.2: The language accepted by a DFA  M=(Q, Σ , δ ,q 0 ,F) is the set of all strings on  Σ   accepted by M.     L(M) = { w ∈Σ *|  δ *(q 0,  w)   F   }  -  δ δ * : total functions  - Complement of L(M)?
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2.1 Deterministic Finite Accepters   Ex 2.2 Find a language L(M)                 q 2  : trap(dead) state                    q 0 q 2 q 1 a a,b a,b b
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2.1 Deterministic Finite Accepters Theorem 2.1 M=(Q, Σ , δ ,q 0 ,F), w ∈Σ + , q i ,q j Q   δ *(q i ,   w)= q j   iff  there is a walk in G M  with  label w from q i  to q j
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10 2.1 Deterministic Finite Accepters Ex 2.3 Find a dfa that recognizes the set of  all strings on  = {a,b} starting with the  Σ prefix ab.
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11 2.1 Deterministic Finite Accepters Ex 2.4 Find a dfa that accepts of all the  strings on  = {0,1}, except those  Σ containing the substring 001.
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2.1 Deterministic Finite Accepters
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This note was uploaded on 11/03/2009 for the course CS automata taught by Professor Prof.jung during the Fall '09 term at 홍익대학교.

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automata-2 - Automata Ch2FiniteAutomata Simpleautomata...

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