Complete problems for deterministic polynomial time

Abstract

The results of Cook and Karp ([K], [C]) aroused considerable interest for at least two reasons. First, the answer to a long-standing open question which had seemed peculiar to automata theory—whether deterministic and nondeterministic polynomial-time-bounded Turing machines are equivalent in power—was seen to be exactly equivalent to determining whether any of several familiar combinatorial problems can be solved by polynomial-time algorithms. Second, the existence of complete problems for NP1 made it possible to replace an entire class of questions by a question about a single representative.Thus all of these combinatorial and automata-theoretic problems were essentially restatements of a single problem, such as: can satisfiability of a propositional formula be decided in polynomial time.