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arXiv · 1309.2394

Polynomial Path Orders

Martin Avanzini·Georg Moser
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Abstract

This paper is concerned with the complexity analysis of constructor term rewrite systems and its ramification in implicit computational complexity. We introduce a path order with multiset status, the polynomial path order POP*, that is applicable in two related, but distinct contexts. On the one hand POP* induces polynomial innermost runtime complexity and hence may serve as a syntactic, and fully automatable, method to analyse the innermost runtime complexity of term rewrite systems. On the other hand POP* provides an order-theoretic characterisation of the polytime computable functions: the polytime computable functions are exactly the functions computable by an orthogonal constructor TRS compatible with POP*.

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Martin Avanzini, Georg Moser. 2013-10-30. Polynomial Path Orders. https://doi.org/10.2168/lmcs-9(4%3A9)2013

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