Solutions to Exercises

Solution Sketch. This is similar to something done in Lecture 7. Let R be the relation that defines an NP search problem. Define the language L that contains all the pairs (x, z) such that z is the prefix of a solution zz′ such that (x, zz′) ∈ R. Under the assumption that P = NP, there is a polynomial time algorithm A that decides L. Now, given x, we can construct a solution y such that (x, y) ∈ R, if such a solution exists, one bit a time using A. (See notes of lecture 7 for more details.)