Abstract
Realizability and reactive synthesis from temporal logics are fundamental problems in the formal verification field. The complexity of the Linear-time Temporal Logic with Past (LTL+P) case led to the definition of fragments with lower complexities and simpler algorithms. Recently, the logic of Extended Bounded Response LTL+P (\(\mathsf {LTL_{EBR}{+}P}\)) has been introduced. It allows one to express any safety language definable in LTL and it is provided with an efficient, fully-symbolic algorithm for reactive synthesis.
In this paper, we extend \(\mathsf {LTL_{EBR}{+}P}\) with fairness conditions, assumptions, and guarantees. The resulting logic, called GR-EBR, preserves the main strength of \(\mathsf {LTL_{EBR}{+}P}\), that is, efficient realizability, and makes it possible to specify properties beyond safety. We study the problem of reactive synthesis for GR-EBR and devise a fully-symbolic algorithm that reduces it to a number of safety subproblems. To ensure soundness and completeness, we propose a general framework for safety reductions in the context of realizability of (fragments of) LTL+P. The experimental evaluation shows the feasibility of the approach.
N. Gigante acknowledges the Free University of Bozen-Bolzano, Faculty of Computer Science RTD project TOTA (Temporal Ontologies and Tableaux Algorithms). The work was partially supported by the Italian GNCS project CATHARSIS (L. Geatti, N. Gigante and A. Montanari).
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Cimatti, A., Geatti, L., Gigante, N., Montanari, A., Tonetta, S. (2021). Fairness, Assumptions, and Guarantees for Extended Bounded Response LTL+P Synthesis. In: Calinescu, R., Păsăreanu, C.S. (eds) Software Engineering and Formal Methods. SEFM 2021. Lecture Notes in Computer Science(), vol 13085. Springer, Cham. https://doi.org/10.1007/978-3-030-92124-8_20
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