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I am taking an algorithm analysis class and am stuck on one of my homework problems and would appreciate it if I could receive some guidance.

The problem I'm stuck on is proving that the empty language and $\{0, 1\}^*$ are the only languages in P that are not complete for P with respect to polynomial-time reductions (problem 34.3-6 in CLRS 3rd edition). The first part of the problem seems fairly straightforward enough (proving the empty language criteria). However, I'm not sure where to even begin when I have to prove the criteria for $\{0, 1\}^*$. I'm NOT looking for the answer, however I would appreciate some guidance on how I can begin to think about this problem.

David Richerby
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user30103927502
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1 Answers1

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Hint. The definition of reduction from $X$ to $Y$ requires that "yes" instances of $X$ be mapped to "yes" instances of $Y$ and "no" instances to "no" instances.

David Richerby
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