I am currently working on the following task:

A language L = {< M> | M(x) = x^2} is given. Now I need to show, that this language is not decidable.
By the way, < M> is the Gödel number

But right now, I don't know how to deal with that task. Honestly, this is the first time that I am working with this kind of task.

I would appreciate if you could give me some hints, because I don't know how to proceed with the task.

  • $\begingroup$ I'd try with a reduction of the halting problem to this, or with Rice's Theorem. $\endgroup$ – G. Bach Dec 8 '13 at 23:33
  • $\begingroup$ @Raphael: Thank you for the hint but my question is not really a duplicate of the question you refer to. The other question asks more generally but this question is more specific(in regarding to a given language). That's all. $\endgroup$ – user11941 Dec 8 '13 at 23:45
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    $\begingroup$ @user2965601, the point is that the techniques there will likely suffice to deal with your task -- so go study the material there in detail. People are not going to spoon-feed you an answer to your exercise, but the answers to that question will help you work out how to solve your exercise on your own. After that, you can see the message before, which says "If those answers do not fully address your question, please ask a new question." (and make sure to explain what you've tried and learned from that other question, and why the techniques shown there do not work for your problem). $\endgroup$ – D.W. Dec 9 '13 at 1:54