An implicit characterization of the polynomial-time decidable sets by cons-free rewriting

Abstract

We define the class of constrained cons-free rewriting systems and show that this class characterizes P, the set of languages decidable in polynomial time on a deterministic Turing machine. The main novelty of the characterization is that it allows very liberal properties of term rewriting, in particular non-deterministic evaluation: no reduction strategy is enforced, and systems are allowed to be non-confluent. © 2014 Springer International Publishing Switzerland.