8 Search Results for "Sickert, Salomon"

Document
DOI: 10.4230/LIPIcs.CONCUR.2024.5
MITL Model Checking via Generalized Timed Automata and a New Liveness Algorithm

Authors: S. Akshay, Paul Gastin, R. Govind, and B. Srivathsan

Published in: LIPIcs, Volume 311, 35th International Conference on Concurrency Theory (CONCUR 2024)

Abstract
The translation of Metric Interval Temporal Logic (MITL) to timed automata is a topic that has been extensively studied. A key challenge here is the conversion of future modalities into equivalent automata. Typical conversions equip the automata with a guess-and-check mechanism to ascertain the truth of future modalities. Guess-and-check can be naturally implemented via alternation. However, since timed automata tools do not handle alternation, existing methods perform an additional step of converting the alternating timed automata into timed automata. This "de-alternation" step proceeds by an intricate finite abstraction of the space of configurations of the alternating automaton. Recently, a model of generalized timed automata (GTA) has been proposed. The model comes with several powerful additional features, and yet, the best known zone-based reachability algorithms for timed automata have been extended to the GTA model, with the same complexity for all the zone operations. An attractive feature of GTAs is the presence of future clocks which act like timers that guess a time to an event and stay alive until a timeout. Future clocks seem to provide another natural way to implement the guess-and-check: start the future clock with a guessed time to an event and check its occurrence using a timeout. Indeed, using this feature, we provide a new concise translation from MITL to GTA. In particular, for the timed until modality, our translation offers an exponential improvement w.r.t. the state-of-the-art. Thanks to this conversion, MITL model checking reduces to checking liveness for GTAs. However, no liveness algorithm is known for GTAs. Due to the presence of future clocks, there is no finite time-abstract bisimulation (region equivalence) for GTAs, whereas liveness algorithms for timed automata crucially rely on the presence of the finite region equivalence. As our second contribution, we provide a new zone-based algorithm for checking Büchi non-emptiness in GTAs, which circumvents this fundamental challenge.
Cite as

S. Akshay, Paul Gastin, R. Govind, and B. Srivathsan. MITL Model Checking via Generalized Timed Automata and a New Liveness Algorithm. In 35th International Conference on Concurrency Theory (CONCUR 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 311, pp. 5:1-5:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{akshay_et_al:LIPIcs.CONCUR.2024.5,
  author =	{Akshay, S. and Gastin, Paul and Govind, R. and Srivathsan, B.},
  title =	{{MITL Model Checking via Generalized Timed Automata and a New Liveness Algorithm}},
  booktitle =	{35th International Conference on Concurrency Theory (CONCUR 2024)},
  pages =	{5:1--5:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-339-3},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{311},
  editor =	{Majumdar, Rupak and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2024.5},
  URN =		{urn:nbn:de:0030-drops-207774},
  doi =		{10.4230/LIPIcs.CONCUR.2024.5},
  annote =	{Keywords: MITL model checking, timed automata, zones, liveness}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2024.15
RobTL: Robustness Temporal Logic for CPS

Authors: Valentina Castiglioni, Michele Loreti, and Simone Tini

Published in: LIPIcs, Volume 311, 35th International Conference on Concurrency Theory (CONCUR 2024)

Abstract
We propose Robustness Temporal Logic (RobTL), a novel temporal logic for the specification and analysis of distances between the behaviours of Cyber-Physical Systems (CPS) over a finite time horizon. RobTL specifications allow us to measure the differences in the behaviours of systems with respect to various objectives and temporal constraints, and to study how those differences evolve in time. Specifically, the unique features of RobTL allow us to specify robustness properties of CPS against uncertainty and perturbations. As an example, we use RobTL to analyse the robustness of an engine system that is subject to attacks aimed at inflicting overstress of equipment.
Cite as

Valentina Castiglioni, Michele Loreti, and Simone Tini. RobTL: Robustness Temporal Logic for CPS. In 35th International Conference on Concurrency Theory (CONCUR 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 311, pp. 15:1-15:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{castiglioni_et_al:LIPIcs.CONCUR.2024.15,
  author =	{Castiglioni, Valentina and Loreti, Michele and Tini, Simone},
  title =	{{RobTL: Robustness Temporal Logic for CPS}},
  booktitle =	{35th International Conference on Concurrency Theory (CONCUR 2024)},
  pages =	{15:1--15:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-339-3},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{311},
  editor =	{Majumdar, Rupak and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2024.15},
  URN =		{urn:nbn:de:0030-drops-207870},
  doi =		{10.4230/LIPIcs.CONCUR.2024.15},
  annote =	{Keywords: Cyber-physical systems, robustness, temporal logic, uncertainty}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2024.24
Validity of Contextual Formulas

Authors: Javier Esparza and Rubén Rubio

Published in: LIPIcs, Volume 311, 35th International Conference on Concurrency Theory (CONCUR 2024)

Abstract
Many well-known logical identities are naturally written as equivalences between contextual formulas. A simple example is the Boole-Shannon expansion c[p] ≡ (p ∧ c[true]) ∨ (¬ p ∧ c[false]), where c denotes an arbitrary formula with possibly multiple occurrences of a "hole", called a context, and c[φ] denotes the result of "filling" all holes of c with the formula φ. Another example is the unfolding rule μX.c[X] ≡ c[μX.c[X]] of the modal μ-calculus. We consider the modal μ-calculus as overarching temporal logic and, as usual, reduce the problem whether φ₁ ≡ φ₂ holds for contextual formulas φ₁, φ₂ to the problem whether φ₁ ↔ φ₂ is valid. We show that the problem whether a contextual formula of the μ-calculus is valid for all contexts can be reduced to validity of ordinary formulas. Our first result constructs a canonical context such that a formula is valid for all contexts iff it is valid for this particular one. However, the ordinary formula is exponential in the nesting-depth of the context variables. In a second result we solve this problem, thus proving that validity of contextual formulas is EXP-complete, as for ordinary equivalences. We also prove that both results hold for CTL and LTL as well. We conclude the paper with some experimental results. In particular, we use our implementation to automatically prove the correctness of a set of six contextual equivalences of LTL recently introduced by Esparza et al. for the normalization of LTL formulas. While Esparza et al. need several pages of manual proof, our tool only needs milliseconds to do the job and to compute counterexamples for incorrect variants of the equivalences.
Cite as

Javier Esparza and Rubén Rubio. Validity of Contextual Formulas. In 35th International Conference on Concurrency Theory (CONCUR 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 311, pp. 24:1-24:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{esparza_et_al:LIPIcs.CONCUR.2024.24,
  author =	{Esparza, Javier and Rubio, Rub\'{e}n},
  title =	{{Validity of Contextual Formulas}},
  booktitle =	{35th International Conference on Concurrency Theory (CONCUR 2024)},
  pages =	{24:1--24:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-339-3},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{311},
  editor =	{Majumdar, Rupak and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2024.24},
  URN =		{urn:nbn:de:0030-drops-207965},
  doi =		{10.4230/LIPIcs.CONCUR.2024.24},
  annote =	{Keywords: \mu-calculus, temporal logic, contextual rules}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2024.28
Faster and Smaller Solutions of Obliging Games

Authors: Daniel Hausmann and Nir Piterman

Published in: LIPIcs, Volume 311, 35th International Conference on Concurrency Theory (CONCUR 2024)

Abstract
Obliging games have been introduced in the context of the game perspective on reactive synthesis in order to enforce a degree of cooperation between the to-be-synthesized system and the environment. Previous approaches to the analysis of obliging games have been small-step in the sense that they have been based on a reduction to standard (non-obliging) games in which single moves correspond to single moves in the original (obliging) game. Here, we propose a novel, large-step view on obliging games, reducing them to standard games in which single moves encode long-term behaviors in the original game. This not only allows us to give a meaningful definition of the environment winning in obliging games, but also leads to significantly improved bounds on both strategy sizes and the solution runtime for obliging games.
Cite as

Daniel Hausmann and Nir Piterman. Faster and Smaller Solutions of Obliging Games. In 35th International Conference on Concurrency Theory (CONCUR 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 311, pp. 28:1-28:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{hausmann_et_al:LIPIcs.CONCUR.2024.28,
  author =	{Hausmann, Daniel and Piterman, Nir},
  title =	{{Faster and Smaller Solutions of Obliging Games}},
  booktitle =	{35th International Conference on Concurrency Theory (CONCUR 2024)},
  pages =	{28:1--28:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-339-3},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{311},
  editor =	{Majumdar, Rupak and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2024.28},
  URN =		{urn:nbn:de:0030-drops-208008},
  doi =		{10.4230/LIPIcs.CONCUR.2024.28},
  annote =	{Keywords: Two-player games, reactive synthesis, Emerson-Lei games, parity games}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2024.13
A Direct Translation from LTL with Past to Deterministic Rabin Automata

Authors: Shaun Azzopardi, David Lidell, and Nir Piterman

Published in: LIPIcs, Volume 306, 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)

Abstract
We present a translation from linear temporal logic with past to deterministic Rabin automata. The translation is direct in the sense that it does not rely on intermediate non-deterministic automata, and asymptotically optimal, resulting in Rabin automata of doubly exponential size. It is based on two main notions. One is that it is possible to encode the history contained in the prefix of a word, as relevant for the formula under consideration, by performing simple rewrites of the formula itself. As a consequence, a formula involving past operators can (through such rewrites, which involve alternating between weak and strong versions of past operators in the formula’s syntax tree) be correctly evaluated at an arbitrary point in the future without requiring backtracking through the word. The other is that this allows us to generalize to linear temporal logic with past the result that the language of a pure-future formula can be decomposed into a Boolean combination of simpler languages, for which deterministic automata with simple acceptance conditions are easily constructed.
Cite as

Shaun Azzopardi, David Lidell, and Nir Piterman. A Direct Translation from LTL with Past to Deterministic Rabin Automata. In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 13:1-13:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{azzopardi_et_al:LIPIcs.MFCS.2024.13,
  author =	{Azzopardi, Shaun and Lidell, David and Piterman, Nir},
  title =	{{A Direct Translation from LTL with Past to Deterministic Rabin Automata}},
  booktitle =	{49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)},
  pages =	{13:1--13:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-335-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{306},
  editor =	{Kr\'{a}lovi\v{c}, Rastislav and Ku\v{c}era, Anton{\'\i}n},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2024.13},
  URN =		{urn:nbn:de:0030-drops-205694},
  doi =		{10.4230/LIPIcs.MFCS.2024.13},
  annote =	{Keywords: Linear temporal logic, \omega-automata, determinization}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2024.35
The Complexity of Simplifying ω-Automata Through the Alternating Cycle Decomposition

Authors: Antonio Casares and Corto Mascle

Published in: LIPIcs, Volume 306, 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)

Abstract
In 2021, Casares, Colcombet and Fijalkow introduced the Alternating Cycle Decomposition (ACD), a structure used to define optimal transformations of Muller into parity automata and to obtain theoretical results about the possibility of relabelling automata with different acceptance conditions. In this work, we study the complexity of computing the ACD and its DAG-version, proving that this can be done in polynomial time for suitable representations of the acceptance condition of the Muller automaton. As corollaries, we obtain that we can decide typeness of Muller automata in polynomial time, as well as the parity index of the languages they recognise. Furthermore, we show that we can minimise in polynomial time the number of colours (resp. Rabin pairs) defining a Muller (resp. Rabin) acceptance condition, but that these problems become NP-complete when taking into account the structure of an automaton using such a condition.
Cite as

Antonio Casares and Corto Mascle. The Complexity of Simplifying ω-Automata Through the Alternating Cycle Decomposition. In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 35:1-35:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{casares_et_al:LIPIcs.MFCS.2024.35,
  author =	{Casares, Antonio and Mascle, Corto},
  title =	{{The Complexity of Simplifying \omega-Automata Through the Alternating Cycle Decomposition}},
  booktitle =	{49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)},
  pages =	{35:1--35:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-335-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{306},
  editor =	{Kr\'{a}lovi\v{c}, Rastislav and Ku\v{c}era, Anton{\'\i}n},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2024.35},
  URN =		{urn:nbn:de:0030-drops-205916},
  doi =		{10.4230/LIPIcs.MFCS.2024.35},
  annote =	{Keywords: Omega-regular languages, Muller automata, Zielonka tree}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2021.123
Optimal Transformations of Games and Automata Using Muller Conditions

Authors: Antonio Casares, Thomas Colcombet, and Nathanaël Fijalkow

Published in: LIPIcs, Volume 198, 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)

Abstract
We consider the following question: given an automaton or a game with a Muller condition, how can we efficiently construct an equivalent one with a parity condition? There are several examples of such transformations in the literature, including in the determinisation of Büchi automata. We define a new transformation called the alternating cycle decomposition, inspired and extending Zielonka’s construction. Our transformation operates on transition systems, encompassing both automata and games, and preserves semantic properties through the existence of a locally bijective morphism. We show a strong optimality result: the obtained parity transition system is minimal both in number of states and number of priorities with respect to locally bijective morphisms. We give two applications: the first is related to the determinisation of Büchi automata, and the second is to give crisp characterisations on the possibility of relabelling automata with different acceptance conditions.
Cite as

Antonio Casares, Thomas Colcombet, and Nathanaël Fijalkow. Optimal Transformations of Games and Automata Using Muller Conditions. In 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 198, pp. 123:1-123:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{casares_et_al:LIPIcs.ICALP.2021.123,
  author =	{Casares, Antonio and Colcombet, Thomas and Fijalkow, Nathana\"{e}l},
  title =	{{Optimal Transformations of Games and Automata Using Muller Conditions}},
  booktitle =	{48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)},
  pages =	{123:1--123:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-195-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{198},
  editor =	{Bansal, Nikhil and Merelli, Emanuela and Worrell, James},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2021.123},
  URN =		{urn:nbn:de:0030-drops-141928},
  doi =		{10.4230/LIPIcs.ICALP.2021.123},
  annote =	{Keywords: Automata over infinite words, Omega regular languages, Determinisation of automata}
}
Document
DOI: 10.4230/LIPIcs.ITP.2019.11
A Verified and Compositional Translation of LTL to Deterministic Rabin Automata

Authors: Julian Brunner, Benedikt Seidl, and Salomon Sickert

Published in: LIPIcs, Volume 141, 10th International Conference on Interactive Theorem Proving (ITP 2019)

Abstract
We present a formalisation of the unified translation approach from linear temporal logic (LTL) to omega-automata from [Javier Esparza et al., 2018]. This approach decomposes LTL formulas into "simple" languages and allows a clear separation of concerns: first, we formalise the purely logical result yielding this decomposition; second, we develop a generic, executable, and expressive automata library providing necessary operations on automata to re-combine the "simple" languages; third, we instantiate this generic theory to obtain a construction for deterministic Rabin automata (DRA). We extract from this particular instantiation an executable tool translating LTL to DRAs. To the best of our knowledge this is the first verified translation of LTL to DRAs that is proven to be double-exponential in the worst case which asymptotically matches the known lower bound.
Cite as

Julian Brunner, Benedikt Seidl, and Salomon Sickert. A Verified and Compositional Translation of LTL to Deterministic Rabin Automata. In 10th International Conference on Interactive Theorem Proving (ITP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 141, pp. 11:1-11:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{brunner_et_al:LIPIcs.ITP.2019.11,
  author =	{Brunner, Julian and Seidl, Benedikt and Sickert, Salomon},
  title =	{{A Verified and Compositional Translation of LTL to Deterministic Rabin Automata}},
  booktitle =	{10th International Conference on Interactive Theorem Proving (ITP 2019)},
  pages =	{11:1--11:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-122-1},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{141},
  editor =	{Harrison, John and O'Leary, John and Tolmach, Andrew},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2019.11},
  URN =		{urn:nbn:de:0030-drops-110664},
  doi =		{10.4230/LIPIcs.ITP.2019.11},
  annote =	{Keywords: Automata Theory, Automata over Infinite Words, Deterministic Automata, Linear Temporal Logic, Model Checking, Verified Algorithms}
}
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