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What is difference between "recognizable" and "decidable" in context of Turing machines?

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up vote 12 down vote accepted

A language is Recognizable iff there is a Turing Machine which will halt and accept only the strings in that language and for strings not in the language, the TM either rejects, or does not halt at all. Note: there is no requirement that the Turing Machine should halt for strings not in the language.

A language is Decidable iff there is a Turing Machine which will accept strings in the language and reject strings not in the language.

Perhaps this link will be helpful: http://kilby.stanford.edu/~rvg/154/handouts/decidability.html

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For a language to be recognizable, you need there to be a machine which accepts all strings in the language, and also fails to accept all strings not in the language. With your definition, all languages are recognizable by the always-accept machine. –  Chris Eagle Mar 8 '11 at 18:15
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@Chris: Was editing... Thanks! –  Aryabhata Mar 8 '11 at 18:16
    
Great to know, thnks, very helpful! had that question in mind and i cldnt find a real difference –  user23259 Jan 19 '12 at 21:21
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