Expressiveness of Extended Bounded Response LTL

Alessandro Cimatti
(Fondazione Bruno Kessler)
Luca Geatti
(University of Udine, Fondazione Bruno Kessler)
Nicola Gigante
(Free University of Bozen-Bolzano)
Angelo Montanari
(University of Udine)
Stefano Tonetta
(Fondazione Bruno Kessler)

Extended Bounded Response LTL with Past (LTLEBR+P) is a safety fragment of Linear Temporal Logic with Past (LTL+P) that has been recently introduced in the context of reactive synthesis. The strength of LTLEBR+P is a fully symbolic compilation of formulas into symbolic deterministic automata. Its syntax is organized in four levels. The first three levels feature (a particular combination of) future temporal modalities, the last one admits only past temporal operators. At the base of such a structuring there are algorithmic motivations: each level corresponds to a step of the algorithm for the automaton construction. The complex syntax of LTLEBR+P made it difficult to precisely characterize its expressive power, and to compare it with other LTL+P safety fragments.

In this paper, we first prove that LTLEBR+P is expressively complete with respect to the safety fragment of LTL+P, that is, any safety language definable in LTL+P can be formalized in LTLEBR+P, and vice versa. From this, it follows that LTLEBR+P and Safety-LTL are expressively equivalent. Then, we show that past modalities play an essential role in LTLEBR+P: we prove that the future fragment of LTLEBR+P is strictly less expressive than full LTLEBR+P.

In Pierre Ganty and Davide Bresolin: Proceedings 12th International Symposium on Games, Automata, Logics, and Formal Verification (GandALF 2021), Padua, Italy, 20-22 September 2021, Electronic Proceedings in Theoretical Computer Science 346, pp. 152–165.
Published: 17th September 2021.

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