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      Memoization for Unary Logic Programming: Characterizing PTIME

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          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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          Journal
          2015-01-21
          2015-02-04
          Article
          1501.05104
          a60f75dc-6a2a-47e1-831e-f06c816dc92f

          http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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          Custom metadata
          Soumis {\`a} LICS 2015
          cs.LO cs.CC math.LO
          ccsd

          Theoretical computer science,Logic & Foundation
          Theoretical computer science, Logic & Foundation

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