On First-order Cons-free Term Rewriting and PTIME

Abstract

In this paper, we prove that (first-order) cons-free term rewriting with a call-by-value reduction strategy exactly characterises the class of PTIME-computable functions. We use this to give an alternative proof of the result by Carvalho and Simonsen which states that cons-free term rewriting with linearity constraints characterises this class.