A New Order-theoretic Characterisation of the Polytime Computable Functions

Martin Avanzini; Naohi Eguchi; Georg Moser

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arXiv · 1201.2553

A New Order-theoretic Characterisation of the Polytime Computable Functions

Martin Avanzini·Naohi Eguchi·Georg Moser

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Abstract

We propose a new order, the small polynomial path order (sPOP* for short). The order sPOP* provides a characterisation of the class of polynomial time computable function via term rewrite systems. Any polynomial time computable function gives rise to a rewrite system that is compatible with sPOP*. On the other hand any function defined by a rewrite system compatible with sPOP* is polynomial time computable. Technically sPOP* is a tamed recursive path order with product status. Its distinctive feature is the precise control provided. For any rewrite system that is compatible with sPOP* that makes use of recursion up to depth d, the (innermost) runtime complexity is bounded from above by a polynomial of degree d.

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BibTeX RIS

Martin Avanzini, Naohi Eguchi, Georg Moser. 2012-01-16. A New Order-theoretic Characterisation of the Polytime Computable Functions. https://arxiv.org/abs/1201.2553

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