Abstract

In earlier work, we have shown that for confluent term rewrite systems, innermost polynomial
runtime complexity induces polytime computability of the functions defined. In this paper, we
generalise this result to full rewriting. For that, we again exploit graph rewriting. We give a new
proof of the adequacy of graph rewriting for full rewriting that allows for a precise control of the
resources copied. In sum we completely describe an implementation of rewriting on a Turing
machine. We show that the runtime complexity with respect to rewrite systems is polynomially
related to the runtime complexity on a Turing machine. Our result strengthens the evidence that
the complexity of a rewrite system is truthfully represented through the length of derivations.
Moreover our result allows the classification of deterministic as well as nondeterministic
polytime-computation based on runtime complexity analysis of rewrite systems.

BibTeX

@inproceedings{MAGM-RTA10,
  author      = "Martin Avanzini and Georg Moser",
  title       = "Closing the Gap Between Runtime Complexity and Polytime
                 Computability",
  booktitle   = "Proceedings of the 21st International Conference on
                 Rewriting Techniques and Applications",
  series      = "Leibniz International Proceedings in Informatics",
  volume      = 6,
  pages       = "33--48",
  year        = 2010
}