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Communication Dans Un Congrès Année : 2016

Unary Resolution: Characterizing Ptime.

Clément Aubert
Marc Bagnol
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  • PersonId : 932230
Thomas Seiller

Résumé

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. This construction stems from an interactive interpretation of the cut-elimination procedure of linear logic known as the geometry of interaction. This framework is restricted to terms (logic programs, rewriting rules) using only unary symbols, and this restriction is shown to be complete for polynomial time computation by encoding pushdown automata. Soundness w.r.t. Ptime is proven thanks to a saturation method similar to the one used for pushdown systems and inspired by the memoization technique. A Ptime-completeness result for a class of logic programming queries that uses only unary function symbols comes as a direct consequence.

Dates et versions

hal-01321239 , version 1 (25-05-2016)

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Citer

Clément Aubert, Marc Bagnol, Thomas Seiller. Unary Resolution: Characterizing Ptime.. Foundations of Software Science and Computation Structures (FOSSACS), Apr 2016, Eindhoven, Netherlands. pp.373-389, ⟨10.1007/978-3-662-49630-5_22⟩. ⟨hal-01321239⟩

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