# L and L’ are Turing-recognizable, prove L is Turing-decidable - PowerPoint PPT Presentation

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L and L’ are Turing-recognizable, prove L is Turing-decidable. M TR. <w>. accept. w. B. accept. w. accept. reject. A. B checks if string w is in L, A checks if w is in L’ M TR halts because w is in either L or L’; B and A are run once.

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L and L’ are Turing-recognizable, prove L is Turing-decidable

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### L and L’ are Turing-recognizable, prove L is Turing-decidable

MTR

<w>

accept

w

B

accept

w

accept

reject

A

• B checks if string w is in L, A checks if w is in L’

• MTR halts because w is in either L or L’; B and A are run once

### Exercise 4.3MS* = {<Z> | Z is a DFA, L(Z) = S*}

MS*

accept

<Z>

reject

<Z>

MEQdfa

reject

<E>

accept

F

• F creates DFA E such that L(E) = S*

• MEQdfa accepts if L(Z) = L(E), rejects otherwise.

• MS* accepts if and only if L(Z) = L(E) if and only if L(Z) = S*

• MS* halts because F, MEQdfa are decidable and run only once

### Exercise 4.2: MT = {<B,E> | B is a DFA, E is a regular expression and B = E }

MT

<B,E>

<B>

accept

accept

MEQdfa

reject

<F>

<E>

reject

D

• D converts regular expression E into equivalent DFA F

• MEQdfa accepts if L(B) = L(F), rejects otherwise

• MT accepts if and only if L(B) = L(F) if and only if L(B) = L(E)

• MT halts since D and MEQdfaare deciable and run once