NFA, DFA, and regular expressions - 204213 Theory of Computation

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Outline Review Nondeterminism Eq. of NFAs and DFAs Closure Reg.Ex. Eq. between Reg.Ex. and FAaWhat about other operations?We prove Theorem 1 by simulating two finite automata withone finite automaton.This approach cannot be used directly to prove that the set ofregular languages is closed under concatenation. Why?For string w ∈ A 1 ◦ A 2 , there exists a pair x and y such thatw = xy and x ∈ A 1 and y ∈ A 2 .To construct a finite automaton M for A 1 ◦ A 2 from M 1 andM 2 that recognize A 1 and A 2 we need to simulate M 1 to theend of x and start simulating M 2 right after that.
Outline Review Nondeterminism Eq. of NFAs and DFAs Closure Reg.Ex. Eq. between Reg.Ex. and FAaWhat about other operations?We prove Theorem 1 by simulating two finite automata withone finite automaton.This approach cannot be used directly to prove that the set ofregular languages is closed under concatenation. Why?For string w ∈ A 1 ◦ A 2 , there exists a pair x and y such thatw = xy and x ∈ A 1 and y ∈ A 2 .To construct a finite automaton M for A 1 ◦ A 2 from M 1 andM 2 that recognize A 1 and A 2 we need to simulate M 1 to theend of x and start simulating M 2 right after that. And it ishard to “tell” where x ends.
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NFA, DFA, and regular expressions - 204213 Theory of Computation

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