Transparency No. 10-1

Formal Language

and Automata Theory

Chapter 10

The Myhill-Nerode Theorem

(lecture 15,16 and B)

The Myhill-Nerode theorem

Transparency No. 10-2

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->

QNs.t.

f(sM) = sN

f(dM(p,a)) = dN(f(p),a) for all p QM, a S

p FMiff 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.

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