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Model-Guided Synthesis for LTL over Finite Traces

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Verification, Model Checking, and Abstract Interpretation (VMCAI 2024)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14499))

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Abstract

Satisfiability and synthesis are two fundamental problems for Linear Temporal Logic, both of which can be solved on the automaton constructed from the input formula. In general, satisfiability is easier than synthesis in both theory and practice, as satisfiability needs only to find a satisfying trace, while synthesis has to find a winning strategy.

This paper presents a novel technique called MoGuS, which improves the performance of synthesis for \(\textsc {LTL}_f\), a variant of LTL interpreted over finite traces, by repeatedly invoking an \(\textsc {LTL}_f\) satisfiability checker to guide its search for a winning strategy. Satiisfiabiity checkers have not been used before in the context of \(\textsc {LTL}_f\) synthesis. MoGuS computes a satisfying trace of the input formula, and then uses the formula-progression technique to compute the states on the fly in the automaton run. It then checks whether there exists a winning strategy from each of the states. If not, the current state is marked as a ‘failure’ state (as it can never produce a winning strategy), the checking rolls back to its predecessor state, and the process repeats. MoGuS returns ‘Realizable’ if the initial state turns out to be winning, and ‘Unrealizable’ otherwise. We conducted an extensive experimental evaluation of MoGuS by comparing it to different state-of-the-art \(\textsc {LTL}_f\) synthesis algorithms on a large set of benchmarks. The results show that MoGuS has the most stable and the best overall performance on the tested benchmarks.

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Data Availability Statement

To support the experimental results, the source code of MoGuSer and benchmarks is available at https://drive.google.com/file/d/1ohOa4Kl4R4br095k-kVJcWV87U5XON5q/view?usp=sharing.

Notes

  1. 1.

    From the preliminary evaluations, our previous synthesizer OLFS [43] performs much worse than other tested tools, so it is excluded in the comparison.

  2. 2.

    See https://spot.lre.epita.fr/man/randltl.1.html.

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Acknowledgements

This work is supported by National Natural Science Foundation of China (Grant #U21B2015 and #62372178), “Digital Silk Road” Shanghai International Joint Lab of Trustworthy Intelligent Software under Grant 22510750100, Shanghai Collaborative Innovation Center of Trusted Industry Internet Software, by US NSF grants IIS-1527668, CCF-1704883, IIS-1830549, CNS-2016656, and by US DoD MURI grant N00014-20-1-2787.

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Authors and Affiliations

  1. East China Normal University, Shanghai, China

    Shengping Xiao, Yongkang Li, Xinyue Huang, Yicong Xu, Jianwen Li & Geguang Pu

  2. Shanghai Trusted Industrial Control Platform Co., Ltd., Shanghai, China

    Geguang Pu

  3. Technion, Haifa, Israel

    Ofer Strichman

  4. Rice University, Houston, USA

    Moshe Y. Vardi

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  1. Shengping Xiao
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Correspondence to Jianwen Li .

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Editors and Affiliations

  1. CISPA Helmholtz Center for Information Security, Saarbrücken, Germany

    Rayna Dimitrova

  2. Tel Aviv University, Tel Aviv, Israel

    Ori Lahav

  3. New York University, New York, NY, USA

    Sebastian Wolff

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Xiao, S. et al. (2024). Model-Guided Synthesis for LTL over Finite Traces. In: Dimitrova, R., Lahav, O., Wolff, S. (eds) Verification, Model Checking, and Abstract Interpretation. VMCAI 2024. Lecture Notes in Computer Science, vol 14499. Springer, Cham. https://doi.org/10.1007/978-3-031-50524-9_9

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