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 saturationmethod 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.
Lecture Notes in Computer Science: 19th International Conference, Fossacs 2016, Held As Part of the European Joint Conferences on Theory and Practice of Software, Etaps 2016, Eindhoven, the Netherlands, April 2–8, 2016, Proceedings, 2016, p. 373-389