Memoization for Unary Logic Programming: Characterizing PTIME

Abstract : We give a characterization of deterministic polynomial time computation based on an algebraic structure called the resolution semiring, whose elements can be understood as logic programs or sets of rewriting rules over first-order terms. More precisely, we study the restriction of this framework to terms (and logic programs, rewriting rules) using only unary symbols. We prove it is complete for polynomial time computation, using an encoding of pushdown automata. We then introduce an algebraic counterpart of the memoization technique in order to show its PTIME soundness. We finally relate our approach and complexity results to complexity of logic programming. As an application of our techniques, we show a PTIME-completeness result for a class of logic programming queries which use only unary function symbols.
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Submitted on : Friday, October 16, 2015 - 10:15:29 PM
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  • HAL Id : hal-01107377, version 3
  • ARXIV : 1501.05104

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Clément Aubert, Marc Bagnol, Thomas Seiller. Memoization for Unary Logic Programming: Characterizing PTIME. [Research Report] RR-8796, INRIA Grenoble - Rhône-Alpes; Université Paris-Est, LACL (EA 4219), UPEC, F-94010 Créteil, France; Aix Marseille Université, CNRS, Centrale Marseille, I2M UMR 7373, 13453, Marseille, France; IHÉS. 2015, pp.28. ⟨hal-01107377v3⟩

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