Modular Complexity Analysis for Term Rewriting

Harald Zankl; Martin Korp

doi:10.2168/LMCS-10(1:19)2014

Harald Zankl ; Martin Korp - Modular Complexity Analysis for Term Rewriting

lmcs:749 - Logical Methods in Computer Science, April 1, 2014, Volume 10, Issue 1 - https://doi.org/10.2168/LMCS-10(1:19)2014

Modular Complexity Analysis for Term RewritingArticle

Authors: Harald Zankl ; Martin Korp

All current investigations to analyze the derivational complexity of term rewrite systems are based on a single termination method, possibly preceded by transformations. However, the exclusive use of direct criteria is problematic due to their restricted power. To overcome this limitation the article introduces a modular framework which allows to infer (polynomial) upper bounds on the complexity of term rewrite systems by combining different criteria.
Since the fundamental idea is based on relative rewriting, we study how matrix interpretations and match-bounds can be used and extended to measure complexity for relative rewriting, respectively. The modular framework is proved strictly more powerful than the conventional setting. Furthermore, the results have been implemented and experiments show significant gains in power.

Comment: 33 pages; Special issue of RTA 2010

https://doi.org/10.2168/LMCS-10(1:19)2014

Source: arXiv.org:1402.0746

Volume: Volume 10, Issue 1

Secondary volumes: Selected Papers of the 21st International Conference on Rewriting Techniques and Applications (RTA 2010)

Published on: April 1, 2014

Imported on: October 29, 2010

Keywords: Computer Science - Logic in Computer Science

Licence: arXiv.org - Non-exclusive license to distribute

Funding:

Source : OpenAIRE Graph

Termination tools: Verification and Optimization; Code: P 18763

Classifications

Mathematics Subject Classification 2020¹

Sources:

[1] zbMATH Open.

Bibliographic References

12 Documents citing this article

Jan-Christoph Kassing;Grigory Vartanyan;Jürgen Giesl, 2024, A Dependency Pair Framework for Relative Termination of Term Rewriting, Lecture notes in computer science, pp. 360-380, 10.1007/978-3-031-63501-4_19, https://doi.org/10.1007/978-3-031-63501-4_19.

Carsten Fuhs, 2019, Transforming Derivational Complexity of Term Rewriting to Runtime Complexity, Lecture notes in computer science, pp. 348-364, 10.1007/978-3-030-29007-8_20.

Hugo Férée;Samuel Hym;Micaela Mayero;Jean-Yves Moyen;David Nowak, 2018, Formal proof of polynomial-time complexity with quasi-interpretations, Kent Academic Repository (University of Kent), pp. 146-157, 10.1145/3167097.

Maciej Bendkowski;Pierre Lescanne, 2018, Combinatorics of Explicit Substitutions, arXiv (Cornell University), pp. 1-12, 10.1145/3236950.3236951, http://arxiv.org/abs/1804.03862.

Hugo Férée;Samuel Hym;Micaela Mayero;Jean-Yves Moyen;David Nowak, 2017, Formal proof of polynomial-time complexity with quasi-interpretations, Proceedings of the 7th ACM SIGPLAN International Conference on Certified Programs and Proofs - CPP 2018, pp. 146-157, 10.1145/3176245.3167097.

Matthias Naaf;Florian Frohn;Marc Brockschmidt;Carsten Fuhs;Jürgen Giesl, 2017, Complexity Analysis for Term Rewriting by Integer Transition Systems, Lecture notes in computer science, pp. 132-150, 10.1007/978-3-319-66167-4_8.

Florian Frohn;Jürgen Giesl;Jera Hensel;Cornelius Aschermann;Thomas Ströder, 2016, Lower Bounds for Runtime Complexity of Term Rewriting, Journal of Automated Reasoning, 59, 1, pp. 121-163, 10.1007/s10817-016-9397-x.

René Thiemann;Akihisa Yamada, 2016, Formalizing Jordan normal forms in Isabelle/HOL, Proceedings of the 5th ACM SIGPLAN Conference on Certified Programs and Proofs, pp. 88-99, 10.1145/2854065.2854073.

Avanzini, Martin;Sternagel, Christian;Thiemann, René, 2015, Certification of Complexity Proofs using CeTA, DROPS (Schloss Dagstuhl – Leibniz Center for Informatics), 10.4230/lipics.rta.2015.23, https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.RTA.2015.23.

Martin Avanzini;Ugo Dal Lago;Georg Moser, 2015, Analysing the complexity of functional programs: higher-order meets first-order, ACM SIGPLAN Notices, 50, 9, pp. 152-164, 10.1145/2858949.2784753.

Martin Avanzini;Ugo Dal Lago;Georg Moser, 2015, Analysing the complexity of functional programs: higher-order meets first-order, SPIRE - Sciences Po Institutional REpository, pp. 152-164, 10.1145/2784731.2784753, https://inria.hal.science/hal-01231809.

Christian Sternagel;René Thiemann, 2014, The Certification Problem Format, Electronic Proceedings in Theoretical Computer Science, 167, pp. 61-72, 10.4204/eptcs.167.8, https://doi.org/10.4204/eptcs.167.8.

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