fa-decidable - 8c Decidable problems of regular languages...

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8c: Decidable problems of regular languages The following decision problems are decidable (solvable), i.e., there exist algorithms for solving these problems. 1. Given a FA M and a string w , does M accept w ? 2. Given a regular expression α and a string w , does α generate w ? 3. Given a FA M , does M accept e ? 4. Given a FA M , is L ( M ) = ? 5. Given a FA M , is L ( M ) = Σ ? 6. Given two FAs M 1 and M 2 , is L ( M 1 ) = L ( M 2 )? 7. Given two FAs M 1 and M 2 , is L ( M 1 ) L ( M 2 )? 1
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1. Given a FA M and a string w , does M accept w ? If the FA is nondeterministic, transform it to an equiv- alent DFA. M reads one symbol from w at a time and moves the tape head one position to the right and enters a new state. Since the tape head always moves right and the string is of finite length, the algorithm must termi- nate. If M is at a final state when the entire string is read, then M accepts w ; otherwise M does not accept w . Thus, the decision problem is decidable.
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