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Documents authored by Peron, Adriano

Document
DOI: 10.4230/LIPIcs.TIME.2024.18
Full Characterisation of Extended CTL*

Authors: Massimo Benerecetti, Laura Bozzelli, Fabio Mogavero, and Adriano Peron

Published in: LIPIcs, Volume 318, 31st International Symposium on Temporal Representation and Reasoning (TIME 2024)

Abstract
The precise identification of the expressive power of logic languages used in formal methods for specifying and verifying run-time properties of critical systems is a fundamental task and characterisation theorems play a crucial role as model-theoretic tools in this regard. While a clear picture of the expressive power of linear-time temporal logics in terms of word automata and predicate logics has long been established, a complete mapping of the corresponding relationships for branching-time temporal logics has proven to be a more elusive task over the past four decades with few scattered results. Only recently, an automata-theoretic characterisation of both CTL* and its full-ω-regular extension ECTL* has been provided in terms of Symmetric Hesitant Tree Automata (HTA), with and without a suitable counter-freeness restriction on their linear behaviours. These two temporal logics also correspond to the bisimulation-invariant semantic fragments of Monadic Path Logic (MPL) and Monadic Chain Logic (MCL), respectively. Additionally, it has been proven that the counting extensions of CTL* and ECTL*, namely CCTL* and CECTL*, enjoy equivalent graded versions of the HTAs for the corresponding non-counting logics. However, while Moller and Rabinovich have proved CCTL* to be equivalent to full MPL, thus filling the gap for the standard branching-time logic, no similar result has been given for CECTL*. This work completes the picture, by proving the expressive equivalence of CECTL* and full MCL, by means of a composition theorem for the latter logic. This also indirectly establishes the equivalence between HTAs and their first-order extensions HFTAs, as originally introduced by Walukiewicz.
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Massimo Benerecetti, Laura Bozzelli, Fabio Mogavero, and Adriano Peron. Full Characterisation of Extended CTL*. In 31st International Symposium on Temporal Representation and Reasoning (TIME 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 318, pp. 18:1-18:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{benerecetti_et_al:LIPIcs.TIME.2024.18,
  author =	{Benerecetti, Massimo and Bozzelli, Laura and Mogavero, Fabio and Peron, Adriano},
  title =	{{Full Characterisation of Extended CTL*}},
  booktitle =	{31st International Symposium on Temporal Representation and Reasoning (TIME 2024)},
  pages =	{18:1--18:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-349-2},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{318},
  editor =	{Sala, Pietro and Sioutis, Michael and Wang, Fusheng},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TIME.2024.18},
  URN =		{urn:nbn:de:0030-drops-212259},
  doi =		{10.4230/LIPIcs.TIME.2024.18},
  annote =	{Keywords: Branching-Time Temporal Logics, Monadic Chain Logic, Tree Automata}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2024.128
Automata-Theoretic Characterisations of Branching-Time Temporal Logics

Authors: Massimo Benerecetti, Laura Bozzelli, Fabio Mogavero, and Adriano Peron

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract
Characterisations theorems serve as important tools in model theory and can be used to assess and compare the expressive power of temporal languages used for the specification and verification of properties in formal methods. While complete connections have been established for the linear-time case between temporal logics, predicate logics, algebraic models, and automata, the situation in the branching-time case remains considerably more fragmented. In this work, we provide an automata-theoretic characterisation of some important branching-time temporal logics, namely CTL* and ECTL* interpreted on arbitrary-branching trees, by identifying two variants of Hesitant Tree Automata that are proved equivalent to those logics. The characterisations also apply to Monadic Path Logic and the bisimulation-invariant fragment of Monadic Chain Logic, again interpreted over trees. These results widen the characterisation landscape of the branching-time case and solve a forty-year-old open question.
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Massimo Benerecetti, Laura Bozzelli, Fabio Mogavero, and Adriano Peron. Automata-Theoretic Characterisations of Branching-Time Temporal Logics. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 128:1-128:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{benerecetti_et_al:LIPIcs.ICALP.2024.128,
  author =	{Benerecetti, Massimo and Bozzelli, Laura and Mogavero, Fabio and Peron, Adriano},
  title =	{{Automata-Theoretic Characterisations of Branching-Time Temporal Logics}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{128:1--128:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.128},
  URN =		{urn:nbn:de:0030-drops-202716},
  doi =		{10.4230/LIPIcs.ICALP.2024.128},
  annote =	{Keywords: Branching-Time Temporal Logics, Monadic Second-Order Logics, Tree Automata}
}
Document
DOI: 10.4230/LIPIcs.TIME.2022.11
A Quantitative Extension of Interval Temporal Logic over Infinite Words

Authors: Laura Bozzelli and Adriano Peron

Published in: LIPIcs, Volume 247, 29th International Symposium on Temporal Representation and Reasoning (TIME 2022)

Abstract
Model checking (MC) for Halpern and Shoham’s interval temporal logic HS has been recently investigated in a systematic way, and it is known to be decidable under three distinct semantics (state-based, trace-based and tree-based semantics), all of them assuming homogeneity in the propositional valuation. Here, we focus on the trace-based semantics, where the main semantic entities are the infinite execution paths (traces) of the given Kripke structure. We introduce a quantitative extension of HS over traces, called Difference HS (DHS), allowing one to express timing constraints on the difference among interval lengths (durations). We show that MC and satisfiability of full DHS are in general undecidable, so, we investigate the decidability border for these problems by considering natural syntactical fragments of DHS. In particular, we identify a maximal decidable fragment DHS_{simple} of DHS proving in addition that the considered problems for this fragment are at least 2Expspace-hard. Moreover, by exploiting new results on linear-time hybrid logics, we show that for an equally expressive fragment of DHS_{simple}, the problems are Expspace-complete. Finally, we provide a characterization of HS over traces by means of the one-variable fragment of a novel hybrid logic.
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Laura Bozzelli and Adriano Peron. A Quantitative Extension of Interval Temporal Logic over Infinite Words. In 29th International Symposium on Temporal Representation and Reasoning (TIME 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 247, pp. 11:1-11:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{bozzelli_et_al:LIPIcs.TIME.2022.11,
  author =	{Bozzelli, Laura and Peron, Adriano},
  title =	{{A Quantitative Extension of Interval Temporal Logic over Infinite Words}},
  booktitle =	{29th International Symposium on Temporal Representation and Reasoning (TIME 2022)},
  pages =	{11:1--11:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-262-4},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{247},
  editor =	{Artikis, Alexander and Posenato, Roberto and Tonetta, Stefano},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TIME.2022.11},
  URN =		{urn:nbn:de:0030-drops-172585},
  doi =		{10.4230/LIPIcs.TIME.2022.11},
  annote =	{Keywords: Interval temporal logic, Homogeneity Assumption, Quantitative Constraints, Model checking, Decision Procedures, Complexity issues, Linear-time Hybrid Logics}
}
Document
DOI: 10.4230/LIPIcs.TIME.2022.14
Taming Strategy Logic: Non-Recurrent Fragments

Authors: Massimo Benerecetti, Fabio Mogavero, and Adriano Peron

Published in: LIPIcs, Volume 247, 29th International Symposium on Temporal Representation and Reasoning (TIME 2022)

Abstract
Strategy Logic (SL for short) is one of the prominent languages for reasoning about the strategic abilities of agents in a multi-agent setting. This logic extends LTL with first-order quantifiers over the agent strategies and encompasses other formalisms, such as ATL* and CTL*. The model-checking problem for SL and several of its fragments have been extensively studied. On the other hand, the picture is much less clear on the satisfiability front, where the problem is undecidable for the full logic. In this work, we study two fragments of One-Goal SL, where the nesting of sentences within temporal operators is constrained. We show that the satisfiability problem for these logics, and for the corresponding fragments of ATL* and CTL*, is ExpSpace and PSpace-Complete, respectively.
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Massimo Benerecetti, Fabio Mogavero, and Adriano Peron. Taming Strategy Logic: Non-Recurrent Fragments. In 29th International Symposium on Temporal Representation and Reasoning (TIME 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 247, pp. 14:1-14:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{benerecetti_et_al:LIPIcs.TIME.2022.14,
  author =	{Benerecetti, Massimo and Mogavero, Fabio and Peron, Adriano},
  title =	{{Taming Strategy Logic: Non-Recurrent Fragments}},
  booktitle =	{29th International Symposium on Temporal Representation and Reasoning (TIME 2022)},
  pages =	{14:1--14:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-262-4},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{247},
  editor =	{Artikis, Alexander and Posenato, Roberto and Tonetta, Stefano},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TIME.2022.14},
  URN =		{urn:nbn:de:0030-drops-172611},
  doi =		{10.4230/LIPIcs.TIME.2022.14},
  annote =	{Keywords: Strategic Reasoning, Multi-Agent Systems, Temporal Logics, Satisfiability}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2022.27
Expressiveness and Decidability of Temporal Logics for Asynchronous Hyperproperties

Authors: Laura Bozzelli, Adriano Peron, and César Sánchez

Published in: LIPIcs, Volume 243, 33rd International Conference on Concurrency Theory (CONCUR 2022)

Abstract
Hyperproperties are properties of systems that relate different executions traces, with many applications from security to symmetry, consistency models of concurrency, etc. In recent years, different linear-time logics for specifying asynchronous hyperproperties have been investigated. Though model checking of these logics is undecidable, useful decidable fragments have been identified with applications e.g. for asynchronous security analysis. In this paper, we address expressiveness and decidability issues of temporal logics for asynchronous hyperproperties. We compare the expressiveness of these logics together with the extension S1S[E] of S1S with the equal-level predicate by obtaining an almost complete expressiveness picture. We also study the expressive power of these logics when interpreted on singleton sets of traces. We show that for two asynchronous extensions of HyperLTL, checking the existence of a singleton model is already undecidable, and for one of them, namely Context HyperLTL (HyperLTL_C), we establish a characterization of the singleton models in terms of the extension of standard FO[<] over traces with addition. This last result generalizes the well-known equivalence between FO[<] and LTL. Finally, we identify new boundaries on the decidability of model checking HyperLTL_C.
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Laura Bozzelli, Adriano Peron, and César Sánchez. Expressiveness and Decidability of Temporal Logics for Asynchronous Hyperproperties. In 33rd International Conference on Concurrency Theory (CONCUR 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 243, pp. 27:1-27:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{bozzelli_et_al:LIPIcs.CONCUR.2022.27,
  author =	{Bozzelli, Laura and Peron, Adriano and S\'{a}nchez, C\'{e}sar},
  title =	{{Expressiveness and Decidability of Temporal Logics for Asynchronous Hyperproperties}},
  booktitle =	{33rd International Conference on Concurrency Theory (CONCUR 2022)},
  pages =	{27:1--27:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-246-4},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{243},
  editor =	{Klin, Bartek and Lasota, S{\l}awomir and Muscholl, Anca},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2022.27},
  URN =		{urn:nbn:de:0030-drops-170905},
  doi =		{10.4230/LIPIcs.CONCUR.2022.27},
  annote =	{Keywords: Hyperproperties, Asynchronous hyperproperties, Temporal logics for hyperproperties, Expressiveness, Decidability, Model checking}
}
Document
DOI: 10.4230/LIPIcs.TIME.2021.9
Pspace-Completeness of the Temporal Logic of Sub-Intervals and Suffixes

Authors: Laura Bozzelli, Angelo Montanari, Adriano Peron, and Pietro Sala

Published in: LIPIcs, Volume 206, 28th International Symposium on Temporal Representation and Reasoning (TIME 2021)

Abstract
In this paper, we establish Pspace-completeness of the finite satisfiability and model checking problems for the fragment of Halpern and Shoham interval logic with modality ⟨E⟩, for the "suffix" relation on pairs of intervals, and modality ⟨D⟩, for the "sub-interval" relation, under the homogeneity assumption. The result significantly improves the Expspace upper bound recently established for the same fragment, and proves the rather surprising fact that the complexity of the considered problems does not change when we add either the modality for suffixes (⟨E⟩) or, symmetrically, the modality for prefixes (⟨B⟩) to the logic of sub-intervals (featuring only ⟨D⟩).
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Laura Bozzelli, Angelo Montanari, Adriano Peron, and Pietro Sala. Pspace-Completeness of the Temporal Logic of Sub-Intervals and Suffixes. In 28th International Symposium on Temporal Representation and Reasoning (TIME 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 206, pp. 9:1-9:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{bozzelli_et_al:LIPIcs.TIME.2021.9,
  author =	{Bozzelli, Laura and Montanari, Angelo and Peron, Adriano and Sala, Pietro},
  title =	{{Pspace-Completeness of the Temporal Logic of Sub-Intervals and Suffixes}},
  booktitle =	{28th International Symposium on Temporal Representation and Reasoning (TIME 2021)},
  pages =	{9:1--9:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-206-8},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{206},
  editor =	{Combi, Carlo and Eder, Johann and Reynolds, Mark},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TIME.2021.9},
  URN =		{urn:nbn:de:0030-drops-147853},
  doi =		{10.4230/LIPIcs.TIME.2021.9},
  annote =	{Keywords: Interval temporal logic, Satisfiability, Model checking}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2020.21
On a Temporal Logic of Prefixes and Infixes

Authors: Laura Bozzelli, Angelo Montanari, Adriano Peron, and Pietro Sala

Published in: LIPIcs, Volume 170, 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)

Abstract
A classic result by Stockmeyer [Stockmeyer, 1974] gives a non-elementary lower bound to the emptiness problem for star-free generalized regular expressions. This result is intimately connected to the satisfiability problem for interval temporal logic, notably for formulas that make use of the so-called chop operator. Such an operator can indeed be interpreted as the inverse of the concatenation operation on regular languages, and this correspondence enables reductions between non-emptiness of star-free generalized regular expressions and satisfiability of formulas of the interval temporal logic of the chop operator under the homogeneity assumption [Halpern et al., 1983]. In this paper, we study the complexity of the satisfiability problem for a suitable weakening of the chop interval temporal logic, that can be equivalently viewed as a fragment of Halpern and Shoham interval logic featuring the operators B, for "begins", corresponding to the prefix relation on pairs of intervals, and D, for "during", corresponding to the infix relation. The homogeneous models of the considered logic naturally correspond to languages defined by restricted forms of regular expressions, that use union, complementation, and the inverses of the prefix and infix relations.
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Laura Bozzelli, Angelo Montanari, Adriano Peron, and Pietro Sala. On a Temporal Logic of Prefixes and Infixes. In 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 170, pp. 21:1-21:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{bozzelli_et_al:LIPIcs.MFCS.2020.21,
  author =	{Bozzelli, Laura and Montanari, Angelo and Peron, Adriano and Sala, Pietro},
  title =	{{On a Temporal Logic of Prefixes and Infixes}},
  booktitle =	{45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)},
  pages =	{21:1--21:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-159-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{170},
  editor =	{Esparza, Javier and Kr\'{a}l', Daniel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2020.21},
  URN =		{urn:nbn:de:0030-drops-126898},
  doi =		{10.4230/LIPIcs.MFCS.2020.21},
  annote =	{Keywords: Interval Temporal Logic, Star-Free Regular Languages, Satisfiability, Complexity}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2019.33
Interval Temporal Logic for Visibly Pushdown Systems

Authors: Laura Bozzelli, Angelo Montanari, and Adriano Peron

Published in: LIPIcs, Volume 150, 39th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2019)

Abstract
In this paper, we introduce and investigate an extension of Halpern and Shoham’s interval temporal logic HS for the specification and verification of branching-time context-free requirements of pushdown systems under a state-based semantics over Kripke structures. Both homogeneity and visibility are assumed. The proposed logic, called nested BHS, supports branching-time both in the past and in the future, and is able to express non-regular properties of linear and branching behaviours of procedural contexts in a natural way. It strictly subsumes well-known linear time context-free extensions of LTL such as CaRet [R. Alur et al., 2004] and NWTL [R. Alur et al., 2007]. The main result is the decidability of the visibly pushdown model-checking problem against nested BHS. The proof exploits a non-trivial automata-theoretic construction.
Cite as

Laura Bozzelli, Angelo Montanari, and Adriano Peron. Interval Temporal Logic for Visibly Pushdown Systems. In 39th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 150, pp. 33:1-33:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{bozzelli_et_al:LIPIcs.FSTTCS.2019.33,
  author =	{Bozzelli, Laura and Montanari, Angelo and Peron, Adriano},
  title =	{{Interval Temporal Logic for Visibly Pushdown Systems}},
  booktitle =	{39th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2019)},
  pages =	{33:1--33:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-131-3},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{150},
  editor =	{Chattopadhyay, Arkadev and Gastin, Paul},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2019.33},
  URN =		{urn:nbn:de:0030-drops-115959},
  doi =		{10.4230/LIPIcs.FSTTCS.2019.33},
  annote =	{Keywords: Pushdown systems, Interval temporal logic, Model checking}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2019.34
Taming the Complexity of Timeline-Based Planning over Dense Temporal Domains

Authors: Laura Bozzelli, Angelo Montanari, and Adriano Peron

Published in: LIPIcs, Volume 150, 39th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2019)

Abstract
The problem of timeline-based planning (TP) over dense temporal domains is known to be undecidable. In this paper, we introduce two semantic variants of TP, called strong minimal and weak minimal semantics, which allow to express meaningful properties. Both semantics are based on the minimality in the time distances of the existentially-quantified time events from the universally-quantified reference event, but the weak minimal variant distinguishes minimality in the past from minimality in the future. Surprisingly, we show that, despite the (apparently) small difference in the two semantics, for the strong minimal one, the TP problem is still undecidable, while for the weak minimal one, the TP problem is just PSPACE-complete. Membership in PSPACE is determined by exploiting a strictly more expressive extension (ECA^+) of the well-known robust class of Event-Clock Automata (ECA) that allows to encode the weak minimal TP problem and to reduce it to non-emptiness of Timed Automata (TA). Finally, an extension of ECA^+ (ECA^{++}) is considered, proving that its non-emptiness problem is undecidable. We believe that the two extensions of ECA (ECA^+ and ECA^{++}), introduced for technical reasons, are actually valuable per sé in the field of TA.
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Laura Bozzelli, Angelo Montanari, and Adriano Peron. Taming the Complexity of Timeline-Based Planning over Dense Temporal Domains. In 39th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 150, pp. 34:1-34:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{bozzelli_et_al:LIPIcs.FSTTCS.2019.34,
  author =	{Bozzelli, Laura and Montanari, Angelo and Peron, Adriano},
  title =	{{Taming the Complexity of Timeline-Based Planning over Dense Temporal Domains}},
  booktitle =	{39th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2019)},
  pages =	{34:1--34:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-131-3},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{150},
  editor =	{Chattopadhyay, Arkadev and Gastin, Paul},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2019.34},
  URN =		{urn:nbn:de:0030-drops-115963},
  doi =		{10.4230/LIPIcs.FSTTCS.2019.34},
  annote =	{Keywords: Timeline-based planning, timed automata, event-clock automata}
}
Document
DOI: 10.4230/LIPIcs.TIME.2019.18
Complexity Analysis of a Unifying Algorithm for Model Checking Interval Temporal Logic

Authors: Laura Bozzelli, Angelo Montanari, and Adriano Peron

Published in: LIPIcs, Volume 147, 26th International Symposium on Temporal Representation and Reasoning (TIME 2019)

Abstract
The model-checking (MC) problem of Halpern and Shoham Interval Temporal Logic (HS) has been recently investigated in some papers and is known to be decidable. An intriguing open question concerns the exact complexity of the problem for full HS: it is at least EXPSPACE-hard, while the only known upper bound is non-elementary and is obtained by exploiting an abstract representation of Kripke structure paths called descriptors. In this paper we generalize the approach by providing a uniform framework for model-checking full HS and meaningful (almost maximal) fragments, where a specialized type of descriptor is defined for each fragment. We then devise a general MC alternating algorithm parameterized by the type of descriptor which has a polynomially bounded number of alternations and whose running time is bounded by the length of minimal representatives of descriptors (certificates). We analyze the time complexity of the algorithm and give, by non-trivial arguments, tight bounds on the length of certificates. For two types of descriptors, we obtain exponential upper and lower bounds which lead to an elementary MC algorithm for the related HS fragments. For the other types of descriptors, we provide non-elementary lower bounds. This last result addresses a question left open in some papers regarding the possibility of fixing an elementary upper bound on the size of the descriptors for full HS.
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Laura Bozzelli, Angelo Montanari, and Adriano Peron. Complexity Analysis of a Unifying Algorithm for Model Checking Interval Temporal Logic. In 26th International Symposium on Temporal Representation and Reasoning (TIME 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 147, pp. 18:1-18:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{bozzelli_et_al:LIPIcs.TIME.2019.18,
  author =	{Bozzelli, Laura and Montanari, Angelo and Peron, Adriano},
  title =	{{Complexity Analysis of a Unifying Algorithm for Model Checking Interval Temporal Logic}},
  booktitle =	{26th International Symposium on Temporal Representation and Reasoning (TIME 2019)},
  pages =	{18:1--18:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-127-6},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{147},
  editor =	{Gamper, Johann and Pinchinat, Sophie and Sciavicco, Guido},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TIME.2019.18},
  URN =		{urn:nbn:de:0030-drops-113768},
  doi =		{10.4230/LIPIcs.TIME.2019.18},
  annote =	{Keywords: Interval temporal logic, Model checking, Complexity and succinctness issues}
}
Document
DOI: 10.4230/LIPIcs.ICALP.2017.120
Satisfiability and Model Checking for the Logic of Sub-Intervals under the Homogeneity Assumption

Authors: Laura Bozzelli, Alberto Molinari, Angelo Montanari, Adriano Peron, and Pietro Sala

Published in: LIPIcs, Volume 80, 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)

Abstract
In this paper, we investigate the finite satisfiability and model checking problems for the logic D of the sub-interval relation under the homogeneity assumption, that constrains a proposition letter to hold over an interval if and only if it holds over all its points. First, we prove that the satisfiability problem for D, over finite linear orders, is PSPACE-complete; then, we show that its model checking problem, over finite Kripke structures, is PSPACE-complete as well.
Cite as

Laura Bozzelli, Alberto Molinari, Angelo Montanari, Adriano Peron, and Pietro Sala. Satisfiability and Model Checking for the Logic of Sub-Intervals under the Homogeneity Assumption. In 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 80, pp. 120:1-120:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{bozzelli_et_al:LIPIcs.ICALP.2017.120,
  author =	{Bozzelli, Laura and Molinari, Alberto and Montanari, Angelo and Peron, Adriano and Sala, Pietro},
  title =	{{Satisfiability and Model Checking for the Logic of Sub-Intervals under the Homogeneity Assumption}},
  booktitle =	{44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)},
  pages =	{120:1--120:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-041-5},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{80},
  editor =	{Chatzigiannakis, Ioannis and Indyk, Piotr and Kuhn, Fabian and Muscholl, Anca},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2017.120},
  URN =		{urn:nbn:de:0030-drops-74703},
  doi =		{10.4230/LIPIcs.ICALP.2017.120},
  annote =	{Keywords: Interval Temporal Logic, Satisfiability, Model Checking, Decidability, Computational Complexity}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2016.26
Interval vs. Point Temporal Logic Model Checking: an Expressiveness Comparison

Authors: Laura Bozzelli, Alberto Molinari, Angelo Montanari, Adriano Peron, and Pietro Sala

Published in: LIPIcs, Volume 65, 36th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2016)

Abstract
Model checking is a powerful method widely explored in formal verification to check the (state-transition) model of a system against desired properties of its behaviour. Classically, properties are expressed by formulas of a temporal logic, such as LTL, CTL, and CTL*. These logics are "point-wise" interpreted, as they describe how the system evolves state-by-state. On the contrary, Halpern and Shoham's interval temporal logic (HS) is "interval-wise" interpreted, thus allowing one to naturally express properties of computation stretches, spanning a sequence of states, or properties involving temporal aggregations, which are inherently "interval-based". In this paper, we study the expressiveness of HS in model checking, in comparison with that of the standard logics LTL, CTL, and CTL*. To this end, we consider HS endowed with three semantic variants: the state-based semantics, introduced by Montanari et al., which allows branching in the past and in the future, the linear-past semantics, allowing branching only in the future, and the linear semantics, disallowing branching. These variants are compared, as for their expressiveness, among themselves and to standard temporal logics, getting a complete picture. In particular, HS with linear (resp., linear-past) semantics is proved to be equivalent to LTL (resp., finitary CTL*).
Cite as

Laura Bozzelli, Alberto Molinari, Angelo Montanari, Adriano Peron, and Pietro Sala. Interval vs. Point Temporal Logic Model Checking: an Expressiveness Comparison. In 36th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 65, pp. 26:1-26:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{bozzelli_et_al:LIPIcs.FSTTCS.2016.26,
  author =	{Bozzelli, Laura and Molinari, Alberto and Montanari, Angelo and Peron, Adriano and Sala, Pietro},
  title =	{{Interval vs. Point Temporal Logic Model Checking: an Expressiveness Comparison}},
  booktitle =	{36th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2016)},
  pages =	{26:1--26:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-027-9},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{65},
  editor =	{Lal, Akash and Akshay, S. and Saurabh, Saket and Sen, Sandeep},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2016.26},
  URN =		{urn:nbn:de:0030-drops-68615},
  doi =		{10.4230/LIPIcs.FSTTCS.2016.26},
  annote =	{Keywords: Interval Temporal Logics, Expressiveness, Model Checking}
}
Document
DOI: 10.4230/LIPIcs.CSL.2015.193
A Model Checking Procedure for Interval Temporal Logics based on Track Representatives

Authors: Alberto Molinari, Angelo Montanari, and Adriano Peron

Published in: LIPIcs, Volume 41, 24th EACSL Annual Conference on Computer Science Logic (CSL 2015)

Abstract
Model checking is commonly recognized as one of the most effective tool in system verification. While it has been systematically investigated in the context of classical, point-based temporal logics, it is still largely unexplored in the interval logic setting. Recently, a non-elementary model checking algorithm for Halpern and Shoham's modal logic of time intervals HS, interpreted over finite Kripke structures, has been proposed, together with a proof of the EXPSPACE-hardness of the problem. In this paper, we devise an EXPSPACE model checking procedure for two meaningful HS fragments. It exploits a suitable contraction technique, that allows one to replace long enough tracks of a Kripke structure by equivalent shorter ones.
Cite as

Alberto Molinari, Angelo Montanari, and Adriano Peron. A Model Checking Procedure for Interval Temporal Logics based on Track Representatives. In 24th EACSL Annual Conference on Computer Science Logic (CSL 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 41, pp. 193-210, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{molinari_et_al:LIPIcs.CSL.2015.193,
  author =	{Molinari, Alberto and Montanari, Angelo and Peron, Adriano},
  title =	{{A Model Checking Procedure for Interval Temporal Logics based on Track Representatives}},
  booktitle =	{24th EACSL Annual Conference on Computer Science Logic (CSL 2015)},
  pages =	{193--210},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-90-3},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{41},
  editor =	{Kreutzer, Stephan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2015.193},
  URN =		{urn:nbn:de:0030-drops-54150},
  doi =		{10.4230/LIPIcs.CSL.2015.193},
  annote =	{Keywords: Interval Temporal Logic, Model Checking, Complexity}
}
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