Unary Resolution: Characterizing Ptime

  • Clément Aubert
  • Marc Bagnol
  • Thomas Seiller
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9634)


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.


Implicit complexity Unary queries Logic programming Geometry of interaction Proof theory Pushdown automata Saturation Memoization 


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Authors and Affiliations

  1. 1.Department of Computer ScienceAppalachian State UniversityBooneUSA
  2. 2.Department of Mathematics and StatisticsUniversity of OttawaOttawaCanada
  3. 3.Department of Computer ScienceUniversity of CopenhagenCopenhagenDenmark

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