Deterministic versus nondeterministic time and lower bound problems

Abstract

Because many problems of general interest have natural nondeterministic algorithms and because computers act deterministically, it is important to understand the relationship between deterministic and nondeterministic time. Specifically, it is important to understand how quickly a deterministic computing device can determine the outcome of a nondeterministic calculation. So far, we have no general techniques that work any better than trying all step-by-step simulations, an exponential method.The most famous question concerning determinism versus nondeterminism is the P = NP question. However, this is a different question than "what is the relationship?" and it is possible that significant progress about the relationship can be achieved without answering the Pv = NP question. Thanks to efficient reductions from Turing machine simulation to SAT, the relationship question can be posed as a question about SAT. The problem of proving a nontrivial lower bound on the time required to solve SAT is just an instance of the larger problem of proving lower bounds for any natural problem. It is suggested that a study of generic problems might be a fruitful approach toward insights on such problems.