Abstract | ||
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Linear Temporal Logic (LTL) is one of the most popular temporal logics, that comes into play in a variety of branches of computer science. Its widespread use is also due to its strong foundational properties. One of them is Kamp's theorem, showing that LTL and the first-order theory of one successor (S1S[FO]) are expressively equivalent. Safety and co-safety languages, where a finite prefix suffices to establish whether a word does not or does belong to the language, respectively, play a crucial role in lowering the complexity of problems like model checking and reactive synthesis for LTL. Safety-LTL (resp., coSafety-LTL) is a fragment of LTL where only universal (resp., existential) temporal modalities are allowed, that recognises safety (resp., co-safety) languages only. In this paper, we introduce a fragment of S1S[FO], called Safety-FO, and its dual coSafety-FO, which are expressively complete with regards to the LTL-definable safety languages. In particular, we prove that they respectively characterise exactly Safety-LTL and coSafety-LTL, a result that joins Kamp's theorem, and provides a clearer view of the charactisations of (fragments of) [IL in terms of first-order languages. In addition, it gives a direct, compact, and self-contained proof that any safety language definable in LTL is definable in Safety-LTL as well. As a by-product, we obtain some interesting results on the expressive power of the weak tomorrow operator of Safety-LTL interpreted over finite and infinite traces. |
Year | DOI | Venue |
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2022 | 10.1007/978-3-030-99253-8_13 | FOUNDATIONS OF SOFTWARE SCIENCE AND COMPUTATION STRUCTURES (FOSSACS 2022) |
DocType | Volume | ISSN |
Conference | 13242 | 0302-9743 |
Citations | PageRank | References |
0 | 0.34 | 0 |
Authors | ||
5 |
Name | Order | Citations | PageRank |
---|---|---|---|
Alessandro Cimatti | 1 | 5064 | 323.15 |
Luca Geatti | 2 | 0 | 0.34 |
Nicola Gigante | 3 | 0 | 0.34 |
Angelo Montanari | 4 | 1535 | 135.04 |
Stefano Tonetta | 5 | 0 | 1.69 |