I have to answer this question as a homework assignment but I am finding very little material to work with. I understand what is a NP-complete problem and what is a restriction. In my opinion, this statement is true, because you can always restrict the problem in order to "make the problem easier". But I'm looking at it with a bird's eye view... Can anyone help me make some progress finding the answer to this question? Any help will be much appreciated.
Does every NP-complete prob. admit a polynomial-time restriction?
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Converting my comment into an answer - consider the "empty problem," a problem whose instance set is empty. Since the empty set is a subset of every set, this problem technically counts as a restriction of any language (including languages not in NP). It's also a problem in P; you can build a polynomial-time TM that always rejects its input. Therefore, every problem in NP has a polynomial-time restriction.
What I'm still curious about, though, is whether every NP problem whose instance set is infinite has a polynomial-time restriction whose instance set is also infinite. That's a more interesting question, IMHO, and I don't currently have an answer.
Hope this helps!