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AUTOMATA - The Myhill-Nerode Theorem - KUMAR 7

Automata

Post: September 1st, 2011
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Lecture slides on:The Myhill-Nerode Theorem, Myhill-Nerode Relations, Relations b/t DFAs and Myhill-Nerode relations, isomorphism, bisimulation,Autobisimulation,
Lecture slides on:The Myhill-Nerode Theorem, Myhill-Nerode Relations, Relations b/t DFAs and Myhill-Nerode relations, isomorphism, bisimulation,Autobisimulation,
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Contents
Formal Language and Automata Theory Chapter 10 The Myhill-Nerode Theorem (lecture 15,16 and B) Transparency No. 10-1 The Myhill-Nerode theorem Isomorphism of DFAs  M = (QM,S,dM,sM,FM), N = (QN,S, dN,sN,FN): two DFAs  M and N are said to be isomorphic if there is a bijection f:QM-> QN s.t. f(sM) = sN f(dM(p,a)) = dN(f(p),a) for all p  QM , a  S p  FM iff f(p)  FN.  I.e., M and N are essentially the same machine up to renaming of states.  facts: 1. Isomorphic DFAs accept the same set. 2. if M and N are any two DFAs w/o inaccessible states accepting the same set, then the quotient automata M/ and N/  are isomorphic 3. The DFA obtained by the collapsing algorithm (lec. 14) is the minimal DFA for the set it accepts, and this DFA is unique up to isomorphism. Transparency No. 10-2 The Myhill-Nerode theorem Myhill-Nerode Relations  R: a regular set, M=(Q, S, d,s,F): a DFA for R w/o inaccessible states.  M induces an equivalence relation M on S* ..

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