Prompt Interval Temporal Logic

Monica, Dario Della; Montanari, Angelo; Murano, Aniello; Sala, Pietro

doi:10.1007/978-3-319-48758-8_14

Cited by 4 publications

(4 citation statements)

References 20 publications

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“…Roughly speaking, PROMPT-LTL extends LTL with the prompteventually operator, which states that an event will happen within the next b time-units, b being an unknown, constant bound. An analogous extension has been proposed for the propositional interval logic of temporal neighborhood PNL in [13].…”

Section: Introductionmentioning

confidence: 99%

Beyond ω-regular languages: ωT-regular expressions and their automata and logic counterparts

Barozzini

Frutos-Escrig

Monica

et al. 2020

Theoretical Computer Science

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Section: Introductionmentioning

confidence: 99%

Beyond ω-regular languages: ωT-regular expressions and their automata and logic counterparts

Barozzini

Frutos-Escrig

Monica

et al. 2020

Theoretical Computer Science

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“…The elegance and expressive power of HS have attracted attention of the temporal and modal communities, as well as many other areas of computer science, AI, philosophy and linguistics, e.g., [Allen 1984;Cau et al 2002;Zhou and Hansen 2004;Cimatti et al 2015;Della Monica et al 2011;Pratt-Hartmann 2005]. However, promising applications have been hampered by the fact, already discovered by Halpern and Shoham [1991], that HS is highly undecidable (for example, validity over Z and R is Π 1 1 -hard).…”

Section: Introductionmentioning

confidence: 99%

Horn Fragments of the Halpern-Shoham Interval Temporal Logic

Bresolin

Kurucz

Muñoz‐Velasco

et al. 2017

ACM Trans. Comput. Logic

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We investigate the satisfiability problem for Horn fragments of the Halpern-Shoham interval temporal logic depending on the type (box or diamond) of the interval modal operators, the type of the underlying linear order (discrete or dense), and the type of semantics for the interval relations (reflexive or irreflexive). For example, we show that satisfiability of Horn formulas with diamonds is undecidable for any type of linear orders and semantics. On the contrary, satisfiability of Horn formulas with boxes is tractable over both discrete and dense orders under the reflexive semantics and over dense orders under the irreflexive semantics, but becomes undecidable over discrete orders under the irreflexive semantics. Satisfiability of binary Horn formulas with both boxes and diamonds is always undecidable under the irreflexive semantics.

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“…Roughly speaking, PROMPT-LTL extends LTL with the prompt-eventually operator, which states that an event will happen within the next b time-units, b being an unknown, constant bound. An analogous extension has been recently proposed for the propositional interval logic of temporal neighborhood PNL [8].…”

Section: Introductionmentioning

confidence: 99%

Beyond ωBS-regular Languages: ωT-regular Expressions and Counter-Check Automata

Monica

Montanari

Sala

2017

Electron. Proc. Theor. Comput. Sci.

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In the last years, various extensions of ω-regular languages have been proposed in the literature, including ωB-regular (ω-regular languages extended with boundedness), ωS-regular (ω-regular languages extended with strict unboundedness), and ωBS-regular languages (the combination of ωB-and ωS-regular ones). While the first two classes satisfy a generalized closure property, namely, the complement of an ωB-regular (resp., ωS-regular) language is an ωS-regular (resp., ωB-regular) one, the last class is not closed under complementation. The existence of non-ωBS-regular languages that are the complements of some ωBS-regular ones and express fairly natural properties of reactive systems motivates the search for other well-behaved classes of extended ω-regular languages. In this paper, we introduce the class of ωT -regular languages, that includes meaningful languages which are not ωBS-regular. We first define it in terms of ωT -regular expressions. Then, we introduce a new class of automata (counter-check automata) and we prove that (i) their emptiness problem is decidable in PTIME and (ii) they are expressive enough to capture ωT -regular languages (whether or not ωT -regular languages are expressively complete with respect to counter-check automata is still an open problem). Finally, we provide an encoding of ωT -regular expressions into S1S+U.

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Prompt Interval Temporal Logic

Cited by 4 publications

References 20 publications

Beyond ω-regular languages: ωT-regular expressions and their automata and logic counterparts

Beyond ω-regular languages: ωT-regular expressions and their automata and logic counterparts

Horn Fragments of the Halpern-Shoham Interval Temporal Logic

Beyond ωBS-regular Languages: ωT-regular Expressions and Counter-Check Automata

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