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Documents authored by Della Monica, Dario

Document
DOI: 10.4230/LIPIcs.MFCS.2026.29
Deciding the Common Fragment of CTL with past and LTL

Authors: Massimo Benerecetti, Dario Della Monica, Angelo Matteo, Fabio Mogavero, and Gabriele Puppis

Published in: LIPIcs, Volume 386, 51st International Symposium on Mathematical Foundations of Computer Science (MFCS 2026)

Abstract
A central goal of language theory is to compare formalisms by understanding both their expressive overlaps and their relative expressive power. One particularly challenging question in this direction is the problem of determining the common fragment of two formalisms F₁ and F₂, that is, effectively characterise the class F₁∩ F₂ of properties that can be expressed in both formalisms. This question can be equally phrased as a decision problem: given a property expressed in F₁ or F₂, decide whether the same property can be also expressed in F₁∩ F₂. A question closely related to this is the membership problem, denoted F₁ ↦ F₂, which asks whether a property expressed in F₁ can be also expressed in F₂. These problems become particularly difficult when branching-time formalisms are involved, in general due to the lack of equivalent algebraic characterizations. In this work, we prove that LTL ∩ PCTL is decidable, where PCTL denotes CTL extended with past operators. We do this by showing that both membership problems, LTL ↦ PCTL and PCTL ↦ LTL, are decidable. The direction PCTL ↦ LTL follows from suitable combinations of known results. The converse direction, LTL ↦ PCTL, requires an automata-theoretic characterisation of PCTL. Specifically, we introduce a new class of automata, called counter-free hesitant weak tree automata (HWT_cf) that capture precisely the expressiveness of PCTL, and that are obtained by combining two orthogonal restrictions on alternating parity tree automata, namely, counter-free hesitancy and weakness. We then prove that, for every word language L defined by an LTL formula, the associated tree language △[L] is recognisable by an HWT_cf if and only if L is recognized by a deterministic Büchi word automaton. Since the latter recognisability problem is known to be decidable, so is the former. This result advances the longstanding open problem of deciding LTL ∩ CTL. Indeed, that problem can now be reduced to PCTL ↦ CTL, that is, the question of when past operators can be eliminated.
Cite as

Massimo Benerecetti, Dario Della Monica, Angelo Matteo, Fabio Mogavero, and Gabriele Puppis. Deciding the Common Fragment of CTL with past and LTL. In 51st International Symposium on Mathematical Foundations of Computer Science (MFCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 386, pp. 29:1-29:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{benerecetti_et_al:LIPIcs.MFCS.2026.29,
  author =	{Benerecetti, Massimo and Della Monica, Dario and Matteo, Angelo and Mogavero, Fabio and Puppis, Gabriele},
  title =	{{Deciding the Common Fragment of CTL with past and LTL}},
  booktitle =	{51st International Symposium on Mathematical Foundations of Computer Science (MFCS 2026)},
  pages =	{29:1--29:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-442-0},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{386},
  editor =	{Kouck\'{y}, Michal and Petrișan, Daniela},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2026.29},
  URN =		{urn:nbn:de:0030-drops-274104},
  doi =		{10.4230/LIPIcs.MFCS.2026.29},
  annote =	{Keywords: Membership problems, tree languages, tree logics, tree automata, Monadic Path Logic, CTL^*, CTL with past}
}
Document
DOI: 10.4230/LIPIcs.TIME.2020.16
Complexity of Qualitative Timeline-Based Planning

Authors: Dario Della Monica, Nicola Gigante, Salvatore La Torre, and Angelo Montanari

Published in: LIPIcs, Volume 178, 27th International Symposium on Temporal Representation and Reasoning (TIME 2020)

Abstract
The timeline-based approach to automated planning was originally developed in the context of space missions. In this approach, problem domains are expressed as systems consisting of independent but interacting components whose behaviors over time, the timelines, are governed by a set of temporal constraints, called synchronization rules. Although timeline-based system descriptions have been successfully used in practice for decades, the research on the theoretical aspects only started recently. In the last few years, some interesting results have been shown concerning both its expressive power and the computational complexity of the related planning problem. In particular, the general problem has been proved to be EXPSPACE-complete. Given the applicability of the approach in many practical scenarios, it is thus natural to ask whether computationally simpler but still expressive fragments can be identified. In this paper, we study the timeline-based planning problem with the restriction that only qualitative synchronization rules, i.e., rules without explicit time bounds in the constraints, are allowed. We show that the problem becomes PSPACE-complete.
Cite as

Dario Della Monica, Nicola Gigante, Salvatore La Torre, and Angelo Montanari. Complexity of Qualitative Timeline-Based Planning. In 27th International Symposium on Temporal Representation and Reasoning (TIME 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 178, pp. 16:1-16:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{dellamonica_et_al:LIPIcs.TIME.2020.16,
  author =	{Della Monica, Dario and Gigante, Nicola and La Torre, Salvatore and Montanari, Angelo},
  title =	{{Complexity of Qualitative Timeline-Based Planning}},
  booktitle =	{27th International Symposium on Temporal Representation and Reasoning (TIME 2020)},
  pages =	{16:1--16:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-167-2},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{178},
  editor =	{Mu\~{n}oz-Velasco, Emilio and Ozaki, Ana and Theobald, Martin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TIME.2020.16},
  URN =		{urn:nbn:de:0030-drops-129847},
  doi =		{10.4230/LIPIcs.TIME.2020.16},
  annote =	{Keywords: Timeline-based planning, qualitative temporal constraints, complexity}
}
Document
DOI: 10.4230/LIPIcs.TIME.2017.11
Evaluation of Temporal Datasets via Interval Temporal Logic Model Checking

Authors: Dario Della Monica, David de Frutos-Escrig, Angelo Montanari, Aniello Murano, and Guido Sciavicco

Published in: LIPIcs, Volume 90, 24th International Symposium on Temporal Representation and Reasoning (TIME 2017)

Abstract
The problem of temporal dataset evaluation consists in establishing to what extent a set of temporal data (histories) complies with a given temporal condition. It presents a strong resemblance with the problem of model checking enhanced with the ability of rating the compliance degree of a model against a formula. In this paper, we solve the temporal dataset evaluation problem by suitably combining the outcomes of model checking an interval temporal logic formula against sets of histories (finite interval models), possibly taking into account domain-dependent measures/criteria, like, for instance, sensitivity, specificity, and accuracy. From a technical point of view, the main contribution of the paper is a (deterministic) polynomial time algorithm for interval temporal logic model checking over finite interval models. To the best of our knowledge, this is the first application of a (truly) interval temporal logic model checking in the area of temporal databases and data mining rather than in the formal verification setting.
Cite as

Dario Della Monica, David de Frutos-Escrig, Angelo Montanari, Aniello Murano, and Guido Sciavicco. Evaluation of Temporal Datasets via Interval Temporal Logic Model Checking. In 24th International Symposium on Temporal Representation and Reasoning (TIME 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 90, pp. 11:1-11:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{dellamonica_et_al:LIPIcs.TIME.2017.11,
  author =	{Della Monica, Dario and de Frutos-Escrig, David and Montanari, Angelo and Murano, Aniello and Sciavicco, Guido},
  title =	{{Evaluation of Temporal Datasets via Interval Temporal Logic Model Checking}},
  booktitle =	{24th International Symposium on Temporal Representation and Reasoning (TIME 2017)},
  pages =	{11:1--11:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-052-1},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{90},
  editor =	{Schewe, Sven and Schneider, Thomas and Wijsen, Jef},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TIME.2017.11},
  URN =		{urn:nbn:de:0030-drops-79280},
  doi =		{10.4230/LIPIcs.TIME.2017.11},
  annote =	{Keywords: Dataset Evaluation, Temporal Databases, Model Checking, Interval Temporal Logics}
}

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