[PDF] all finite languages are decidable proof

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  • Are all finite languages decidable?

    If A is finite, it is decidable because all finite languages are decidable (just hardwire each of the strings into the TM).23 fév. 2007

  • How do you prove languages are decidable?

    To show that a language is decidable, we need to create a Turing machine which will halt on any input string from the language's alphabet. Since M is a dfa, we already have the Turing Machine and just need to show that the dfa halts on every input.

  • Are finite automata decidable?

    Conclusion: The equivalence problem of finite automata is decidable and decision problem.

  • The proof goes something like this:

    1If A is a finite language, then it contains a finite number of strings a0,a1,?,an.2The language {ai} consisting of a single literal string ai is regular.3The union of a finite number of regular languages is also regular.4Therefore, A={a0}?{a1}???{an} is regular.
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