Transparency No. 10-1
and Automata Theory
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->
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
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.