Closing the Gap Between Runtime Complexity and Polytime Computability
نویسندگان
چکیده
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.
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