The Complexity of Generalized Satisfiability for Linear Temporal Logic

Michael Bauland; Thomas Schneider; Henning Schnoor; Ilka Schnoor; Heribert Vollmer

doi:10.2168/LMCS-5(1:1)2009

Michael Bauland ; Thomas Schneider ; Henning Schnoor ; Ilka Schnoor ; Heribert Vollmer - The Complexity of Generalized Satisfiability for Linear Temporal Logic

lmcs:1158 - Logical Methods in Computer Science, January 26, 2009, Volume 5, Issue 1 - https://doi.org/10.2168/LMCS-5(1:1)2009

The Complexity of Generalized Satisfiability for Linear Temporal LogicArticle

Authors: Michael Bauland ; Thomas Schneider ; Henning Schnoor ; Ilka Schnoor ; Heribert Vollmer

In a seminal paper from 1985, Sistla and Clarke showed that satisfiability for Linear Temporal Logic (LTL) is either NP-complete or PSPACE-complete, depending on the set of temporal operators used. If, in contrast, the set of propositional operators is restricted, the complexity may decrease. This paper undertakes a systematic study of satisfiability for LTL formulae over restricted sets of propositional and temporal operators. Since every propositional operator corresponds to a Boolean function, there exist infinitely many propositional operators. In order to systematically cover all possible sets of them, we use Post's lattice. With its help, we determine the computational complexity of LTL satisfiability for all combinations of temporal operators and all but two classes of propositional functions. Each of these infinitely many problems is shown to be either PSPACE-complete, NP-complete, or in P.

https://doi.org/10.2168/LMCS-5(1:1)2009

Source: arXiv.org:0812.4848

Volume: Volume 5, Issue 1

Published on: January 26, 2009

Imported on: March 28, 2008

Keywords: Computer Science - Logic in Computer Science,F.4.1

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

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Mathematics Subject Classification 2020¹

Sources:

[1] zbMATH Open.

Bibliographic References

16 Documents citing this article

Marcin Dziubiński, 2021, Modal context restriction for multiagent BDI logics, Artificial Intelligence Review, 55, 4, pp. 3075-3151, 10.1007/s10462-021-10064-6, https://doi.org/10.1007/s10462-021-10064-6.

Simon Jantsch;David Müller;Christel Baier;Joachim Klein, 2021, From LTL to unambiguous Büchi automata via disambiguation of alternating automata, Formal Methods in System Design, 58, 1-2, pp. 42-82, 10.1007/s10703-021-00379-z, https://doi.org/10.1007/s10703-021-00379-z.

Yasir Mahmood;Arne Meier;Johannes Schmidt, 2020, Parameterized complexity of abduction in Schaefer’s framework, Journal of Logic and Computation, 31, 1, pp. 266-296, 10.1093/logcom/exaa079.

Pavithra Prabhakar;Ratan Lal;James Kapinski, 2018 IEEE Real-Time Systems Symposium (RTSS), Automatic Trace Generation for Signal Temporal Logic, pp. 208-217, 2018, Nashville, TN, 10.1109/rtss.2018.00038.

Carlo A. Furia;Paola Spoletini, 2016, Bounded variability of metric temporal logic, Annals of Mathematics and Artificial Intelligence, 80, 3-4, pp. 283-316, 10.1007/s10472-016-9532-8, https://doi.org/10.1007/s10472-016-9532-8.

Andreas Krebs;Arne Meier;Martin Mundhenk, arXiv (Cornell University), The Model Checking Fingerprints of CTL Operators, pp. 101-110, 2015, Kassel, Germany, 10.1109/time.2015.13, https://arxiv.org/abs/1504.04708.

Alessandro Artale;Roman Kontchakov;Vladislav Ryzhikov;Michael Zakharyaschev, 2014, A Cookbook for Temporal Conceptual Data Modelling with Description Logics, BIROn (Birkbeck, University of London), 15, 3, pp. 1-50, 10.1145/2629565, https://eprints.bbk.ac.uk/id/eprint/7095/1/7095.pdf.

Carlo A. Furia;Paola Spoletini, arXiv (Cornell University), Bounded Variability of Metric Temporal Logic, pp. 155-163, 2014, Verona, Italy, 10.1109/time.2014.18, http://arxiv.org/abs/1306.2141.

Alessandro Artale;Roman Kontchakov;Vladislav Ryzhikov;Michael Zakharyaschev, BIROn (Birkbeck, University of London), The Complexity of Clausal Fragments of LTL, pp. 35-52, 2013, 10.1007/978-3-642-45221-5_3, https://eprints.bbk.ac.uk/id/eprint/10334/1/lpar13-final.pdf.

Michael Thomas, 2012, On the applicability of Postʼs lattice, arXiv (Cornell University), 112, 10, pp. 386-391, 10.1016/j.ipl.2012.02.002, https://arxiv.org/abs/1007.2924.

Nadia Creignou;Arne Meier;Heribert Vollmer;Michael Thomas, 2012, The Complexity of Reasoning for Fragments of Autoepistemic Logic, Leibniz-Zentrum für Informatik (Schloss Dagstuhl), 13, 2, pp. 1-22, 10.1145/2159531.2159539, https://drops.dagstuhl.de/opus/volltexte/2010/2523/.

Nadia Creignou;Heribert Vollmer, CiteSeer X (The Pennsylvania State University), Parameterized Complexity of Weighted Satisfiability Problems, pp. 341-354, 2012, 10.1007/978-3-642-31612-8_26, http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.639.8312.

Simone Bova, 2012, Lewis Dichotomies in Many-Valued Logics, Studia Logica, 100, 6, pp. 1271-1290, 10.1007/s11225-012-9450-7.

Arne Meier;Thomas Schneider, Lecture notes in computer science, Generalized Satisfiability for the Description Logic $\mathcal{ALC}$, pp. 552-562, 2011, 10.1007/978-3-642-20877-5_53.

Lars Kuhtz;Bernd Finkbeiner, Lecture notes in computer science, Weak Kripke Structures and LTL, pp. 419-433, 2011, 10.1007/978-3-642-23217-6_28.

Viktor Schuppan, 2010, Towards a notion of unsatisfiable and unrealizable cores for LTL, Science of Computer Programming, 77, 7-8, pp. 908-939, 10.1016/j.scico.2010.11.004, https://doi.org/10.1016/j.scico.2010.11.004.

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