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

MTR

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 3 m s z z is a dfa l z s
Exercise 4.3MS* = { | Z is a DFA, L(Z) = S*}

MS*

accept

reject

MEQdfa

reject

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 m t b e b is a dfa e is a regular expression and b e
Exercise 4.2: MT = { | B is a DFA, E is a regular expression and B = E }

MT

accept

accept

MEQdfa

reject

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
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