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International Workshop on Reachability Problems

RP 2017: Reachability Problems pp 87–100Cite as

Model Checking CTL over Restricted Classes of Automatic Structures

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10506))

Abstract

Interpreting formulas over infinite-state relational structures whose states are words over some alphabet and whose relations are recognised by transducers is known under the term “automatic structures” in the world of predicate logic, or as “regular model checking” in formal verification. Both approaches use synchronised transducers, i.e. finite automata reading tuples of letters in each step. This is a strong transducer model with high expressive power leading to undecidability of model checking for any specification language that can express transitive closure.

We develop conditions on a class of binary word relations which are sufficient for the CTL model checking problem to be computable over the class of automatic structures generated by such relations. As an example, we consider recognisable relations. This is an interesting model from an algebraic point of view but it is also far less expressive than those given by synchronised transducers. As a consequence of the weaker expressive power we obtain that this class satisfies the aforementioned sufficient conditions, hence we obtain a decidability result for CTL model checking over a restricted class of infinite-state automatic structures.

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Authors and Affiliations

  1. University of Kassel, Kassel, Germany

    Norbert Hundeshagen & Martin Lange

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  1. Norbert Hundeshagen
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  2. Martin Lange
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Correspondence to Norbert Hundeshagen .

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Editors and Affiliations

  1. Royal Holloway University of London, London, United Kingdom

    Matthew Hague

  2. University of Liverpool, Liverpool, United Kingdom

    Igor Potapov

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Hundeshagen, N., Lange, M. (2017). Model Checking CTL over Restricted Classes of Automatic Structures. In: Hague, M., Potapov, I. (eds) Reachability Problems. RP 2017. Lecture Notes in Computer Science(), vol 10506. Springer, Cham. https://doi.org/10.1007/978-3-319-67089-8_7

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  • DOI: https://doi.org/10.1007/978-3-319-67089-8_7

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