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Model Checking Strategies from Synthesis over Finite Traces

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Automated Technology for Verification and Analysis (ATVA 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14215))

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Abstract

The innovations in reactive synthesis from Linear Temporal Logics over finite traces (\(\textsf{LTLf}\)) will be amplified by the ability to verify the correctness of the strategies generated by \(\textsf{LTLf}\) synthesis tools. This motivates our work on \(\textsf{LTLf}\) model checking. \(\textsf{LTLf}\) model checking, however, is not straightforward. The strategies generated by \(\textsf{LTLf}\) synthesis may be represented using terminating transducers or non-terminating transducers where executions are of finite-but-unbounded length or infinite length, respectively. For synthesis, there is no evidence that one type of transducer is better than the other since they both demonstrate the same complexity and similar algorithms.

In this work, we show that for model checking, the two types of transducers are fundamentally different. Our central result is that \(\textsf{LTLf}\) model checking of non-terminating transducers is exponentially harder than that of terminating transducers. We show that the problems are EXPSPACE-complete and \(\textsf {PSPACE}\)-complete, respectively. Hence, considering the feasibility of verification, \(\textsf{LTLf}\) synthesis tools should synthesize terminating transducers. This is, to the best of our knowledge, the first evidence to use one transducer over the other in \(\textsf{LTLf}\) synthesis.

A. Wells—Work was performed while the author was at Rice University.

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Acknowledgements

We thank the anonymous reviewers for their valuable feedback. This work has been supported by the Engineering and Physical Sciences Research Council [grant number EP/X021513/1], NASA 80NSSC17K0162, NSF grants IIS-1527668, CCF-1704883, IIS-1830549, CNS-2016656, DoD MURI grant N00014-20-1-2787, and an award from the Maryland Procurement Office.

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Authors and Affiliations

  1. Georgia Institute of Technology, Atlanta, GA, USA

    Suguman Bansal

  2. University of Liverpool, Liverpool, UK

    Yong Li

  3. Runtime Verification, Champaign, Illinois, USA

    Lucas M. Tabajara

  4. Rice University, Houston, TX, USA

    Moshe Y. Vardi & Andrew Wells

Authors
  1. Suguman Bansal
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  2. Yong Li
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  3. Lucas M. Tabajara
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  4. Moshe Y. Vardi
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  5. Andrew Wells
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Corresponding authors

Correspondence to Suguman Bansal , Yong Li , Lucas M. Tabajara , Moshe Y. Vardi or Andrew Wells .

Editor information

Editors and Affiliations

  1. Université Sorbonne Paris Nord, Villetaneuse, France

    Étienne André

  2. Singapore Management University, Singapore, Singapore

    Jun Sun

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Bansal, S., Li, Y., Tabajara, L.M., Vardi, M.Y., Wells, A. (2023). Model Checking Strategies from Synthesis over Finite Traces. In: André, É., Sun, J. (eds) Automated Technology for Verification and Analysis. ATVA 2023. Lecture Notes in Computer Science, vol 14215. Springer, Cham. https://doi.org/10.1007/978-3-031-45329-8_11

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  • DOI: https://doi.org/10.1007/978-3-031-45329-8_11

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