self doubt

Question

L1={<M>|M is Tm machine and L(M)=phi} is what language Is it RE or REC Not RE or RE but not Rec??

Comments

I think if nothing there to accept then run for 1 step and halt ==> recursive !

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Hemanth_13 turing machine doesnt accept phii for any language. okk so it is recursive means we can say no directly .

 

 

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I'm not getting you Deepanshu, as there is nothing to accept I want to run the machine for one step then and  say no for any input Could help me where I'm wrong

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Hemanth_13 suppose nothing is there then are u going to accept phi then ??

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No that's why I am running the input string for one step.

Answer 1

It is an RE language but not REC because we need to check membership of each string.  Here domain of the string is all the string.  And since TM accepts nothing so we need to show that entire universe of string is rejected by TM.  And we cant do that because there are infinite strings.