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GR(1)*: GR(1) Specifications Extended with Existential Guarantees

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Formal Methods – The Next 30 Years (FM 2019)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 11800))

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Abstract

Reactive synthesis is an automated procedure to obtain a correct-by-construction reactive system from its temporal logic specification. GR(1) is an expressive assume-guarantee fragment of LTL that enables efficient synthesis and has been recently used in different contexts and application domains. A common form of providing the system’s requirements is through use cases, which are existential in nature. However, GR(1), as a fragment of LTL, is limited to universal properties.

In this paper we introduce GR(1)*, which extends GR(1) with existential guarantees. We show that GR(1)* is strictly more expressive than GR(1) as it enables the expression of guarantees that are inexpressible in LTL. We solve the realizability problem for GR(1)* and present a symbolic strategy construction algorithm for GR(1)* specifications. Importantly, in comparison to GR(1), GR(1)* remains efficient, and induces only a minor additional cost in terms of time complexity, proportional to the extended length of the formula.

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Notes

  1. 1.

    In fact, they are equal, but we do not use this observation in the correctness proof of the algorithm.

  2. 2.

    Even though the algorithm is deterministic, we performed multiple runs since JVM garbage collection and the default automatic variable reordering of CUDD add variance to running times.

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Acknowledgements

This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 638049, SYNTECH).

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Authors and Affiliations

  1. Tel Aviv University, Tel Aviv, Israel

    Gal Amram, Shahar Maoz & Or Pistiner

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  1. Gal Amram
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Correspondence to Shahar Maoz .

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Editors and Affiliations

  1. Consiglio Nazionale delle Ricerche, Pisa, Italy

    Maurice H. ter Beek

  2. Macquarie University, Sydney, NSW, Australia

    Annabelle McIver

  3. University of Minho, Braga, Portugal

    José N. Oliveira

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Amram, G., Maoz, S., Pistiner, O. (2019). GR(1)*: GR(1) Specifications Extended with Existential Guarantees. In: ter Beek, M., McIver, A., Oliveira, J. (eds) Formal Methods – The Next 30 Years. FM 2019. Lecture Notes in Computer Science(), vol 11800. Springer, Cham. https://doi.org/10.1007/978-3-030-30942-8_7

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