research-article

Zeno, Hercules, and the Hydra: Safety Metric Temporal Logic is Ackermann-Complete

Authors:

Joël Ouaknine,

James WorrellAuthors Info & Claims

ACM Transactions on Computational Logic (TOCL), Volume 17, Issue 3

Article No.: 16, Pages 1 - 27

https://doi.org/10.1145/2874774

Published: 17 February 2016 Publication History

Abstract

Metric temporal logic (MTL) is one of the most prominent specification formalisms for real-time systems. Over infinite timed words, full MTL is undecidable, but satisfiability for a syntactially defined safety fragment, called safety MTL, was proved decidable several years ago. Satisfiability for safety MTL is also known to be equivalent to a fair termination problem for a class of channel machines with insertion errors. However, hitherto, its precise computational complexity has remained elusive, with only a nonelementary lower bound. Via another equivalent problem, namely termination for a class of rational relations, we show that satisfiability for safety MTL is Ackermann-complete (i.e., among the easiest nonprimitive recursive problems). This is surprising since decidability was originally established using Higman’s Lemma, suggesting a much higher nonmultiply recursive complexity.

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Cited By

Feng SCarapelle CGil OQuaas K(2019)MTL and TPTL for One-Counter MachinesACM Transactions on Computational Logic10.1145/337278921:2(1-34)Online publication date: 20-Dec-2019
https://dl.acm.org/doi/10.1145/3372789
Lazić RSchmitz SKoskinen EGrohe MShankar N(2016)The Complexity of Coverability in ν-Petri NetsProceedings of the 31st Annual ACM/IEEE Symposium on Logic in Computer Science10.1145/2933575.2933593(467-476)Online publication date: 5-Jul-2016
https://dl.acm.org/doi/10.1145/2933575.2933593
Lazić RTotzke P(2016)What Makes Petri Nets Harder to Verify: Stack or Data?Concurrency, Security, and Puzzles10.1007/978-3-319-51046-0_8(144-161)Online publication date: 18-Dec-2016
https://doi.org/10.1007/978-3-319-51046-0_8

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cover image ACM Transactions on Computational Logic

ACM Transactions on Computational Logic Volume 17, Issue 3

July 2016

233 pages

ISSN:1529-3785

EISSN:1557-945X

DOI:10.1145/2894199

Editor:
Orna Kupferman
School of Computer Science and Engineering, Hebrew University, Israel

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Copyright © 2016 ACM.

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Publication History

Published: 17 February 2016

Accepted: 01 November 2015

Revised: 01 August 2015

Received: 01 April 2015

Published in TOCL Volume 17, Issue 3

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Cited By

Feng SCarapelle CGil OQuaas K(2019)MTL and TPTL for One-Counter MachinesACM Transactions on Computational Logic10.1145/337278921:2(1-34)Online publication date: 20-Dec-2019
https://dl.acm.org/doi/10.1145/3372789
Lazić RSchmitz SKoskinen EGrohe MShankar N(2016)The Complexity of Coverability in ν-Petri NetsProceedings of the 31st Annual ACM/IEEE Symposium on Logic in Computer Science10.1145/2933575.2933593(467-476)Online publication date: 5-Jul-2016
https://dl.acm.org/doi/10.1145/2933575.2933593
Lazić RTotzke P(2016)What Makes Petri Nets Harder to Verify: Stack or Data?Concurrency, Security, and Puzzles10.1007/978-3-319-51046-0_8(144-161)Online publication date: 18-Dec-2016
https://doi.org/10.1007/978-3-319-51046-0_8

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