Unary resolution: characterizing PTIME

Clément Aubert; Marc Bagnol; Thomas Seiller

doi:10.1007/978-3-662-49630-5_22

Unary resolution: characterizing PTIME

Clément Aubert, Marc Bagnol, Thomas Seiller^*

^*Corresponding author for this work

Department of Computer Science

3 Citations (Scopus)

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. 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.

Original language	English
Title of host publication	Foundations of Software Science and Computation Structures : 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
Editors	Bart Jacobs, Christof Löding
Number of pages	17
Publisher	Springer
Publication date	2016
Pages	373-389
DOIs	https://doi.org/10.1007/978-3-662-49630-5_22
Publication status	Published - 2016
Event	19th International Conference on Foundations of Software Science and Computation Structures - Eindhoven, Netherlands Duration: 2 Apr 2016 → 8 Apr 2016 Conference number: 19

Conference

Conference	19th International Conference on Foundations of Software Science and Computation Structures
Number	19
Country/Territory	Netherlands
City	Eindhoven
Period	02/04/2016 → 08/04/2016

Series	Lecture notes in computer science
Volume	9634
ISSN	0302-9743

Keywords

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

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10.1007/978-3-662-49630-5_22

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Aubert, C., Bagnol, M., & Seiller, T. (2016). Unary resolution: characterizing PTIME. In B. Jacobs, & C. Löding (Eds.), Foundations of Software Science and Computation Structures: 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 (pp. 373-389). Springer. Lecture notes in computer science Vol. 9634 https://doi.org/10.1007/978-3-662-49630-5_22

Unary resolution : characterizing PTIME. / Aubert, Clément; Bagnol, Marc; Seiller, Thomas.

Foundations of Software Science and Computation Structures: 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. ed. / Bart Jacobs; Christof Löding. Springer, 2016. p. 373-389 (Lecture notes in computer science, Vol. 9634).

Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review

Aubert, C, Bagnol, M & Seiller, T 2016, Unary resolution: characterizing PTIME. in B Jacobs & C Löding (eds), Foundations of Software Science and Computation Structures: 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. Springer, Lecture notes in computer science, vol. 9634, pp. 373-389, 19th International Conference on Foundations of Software Science and Computation Structures, Eindhoven, Netherlands, 02/04/2016. https://doi.org/10.1007/978-3-662-49630-5_22

Aubert C, Bagnol M, Seiller T. Unary resolution: characterizing PTIME. In Jacobs B, Löding C, editors, Foundations of Software Science and Computation Structures: 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. Springer. 2016. p. 373-389. (Lecture notes in computer science, Vol. 9634). doi: 10.1007/978-3-662-49630-5_22

Aubert, Clément ; Bagnol, Marc ; Seiller, Thomas. / Unary resolution : characterizing PTIME. Foundations of Software Science and Computation Structures: 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. editor / Bart Jacobs ; Christof Löding. Springer, 2016. pp. 373-389 (Lecture notes in computer science, Vol. 9634).

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Unary resolution: characterizing PTIME

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