DROPS

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DOI: 10.4230/LIPIcs.FSTTCS.2025.5

Distributed Games with a Central Decision Maker

Authors: Bharat Adsul and Nehul Jain

Published in: LIPIcs, Volume 360, 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)

Abstract

We study distributed games played on non-deterministic asynchronous automata which feature a central decision maker process that participates in all key decision making tasks. In these partial-information games, processes use their causal past to respond to scheduling choices made by the scheduler and cooperatively strategize as a team to achieve the winning objective. We show that the problem of deciding the existence of a distributed winning strategy is efficiently solvable for global safety and local parity objectives. We provide algorithmic solutions that match their computational hardness. We formulate the notion of a finite-state distributed strategy which allows to quantify its distributed memory requirements. For the aforementioned objectives, we establish that finite-state distributed winning strategies always exist. In fact, we provide novel constructions of such winning strategies which are shown to have almost optimal amount of distributed memory. We also show that a natural extension of the model with two decision making processes is undecidable.

Cite as

Bharat Adsul and Nehul Jain. Distributed Games with a Central Decision Maker. In 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 360, pp. 5:1-5:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{adsul_et_al:LIPIcs.FSTTCS.2025.5,
  author =	{Adsul, Bharat and Jain, Nehul},
  title =	{{Distributed Games with a Central Decision Maker}},
  booktitle =	{45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)},
  pages =	{5:1--5:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-406-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{360},
  editor =	{Aiswarya, C. and Mehta, Ruta and Roy, Subhajit},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2025.5},
  URN =		{urn:nbn:de:0030-drops-250843},
  doi =		{10.4230/LIPIcs.FSTTCS.2025.5},
  annote =	{Keywords: Mazurkiewicz traces, models of concurrency, distributed synthesis, game-theoretic models, asynchronous automata, distributed decision-making}
}

Document

DOI: 10.4230/LIPIcs.FSTTCS.2025.52

Unreliability in Practical Subclasses of Communicating Systems

Authors: Amrita Suresh and Nobuko Yoshida

Published in: LIPIcs, Volume 360, 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)

Abstract

Systems of communicating automata are prominent models for peer-to-peer message-passing over unbounded channels, but in the general scenario, most verification properties are undecidable. To address this issue, two decidable subclasses, Realisable with Synchronous Communication (RSC) and k-Multiparty Compatibility (k-MC), were proposed in the literature, with corresponding verification tools developed and applied in practice. Unfortunately, both RSC and k-MC are not resilient under failures: (1) their decidability relies on the assumption of perfect channels and (2) most standard protocols do not satisfy RSC or k-MC under failures. To address these limitations, this paper studies the resilience of RSC and k-MC under two distinct failure models: interference and crash-stop failures. For interference, we relax the conditions of RSC and k-MC and prove that the inclusions of these relaxed properties remain decidable under interference, preserving their known complexity bounds. We then propose a novel crash-handling communicating system that captures wider behaviours than existing multiparty session types (MPST) with crash-stop failures. We study a translation of MPST with crash-stop failures into this system integrating RSC and k-MC properties, and establish their decidability results. Finally, by verifying representative protocols from the literature using RSC and k-MC tools extended to interferences, we evaluate the relaxed systems and demonstrate their resilience.

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Amrita Suresh and Nobuko Yoshida. Unreliability in Practical Subclasses of Communicating Systems. In 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 360, pp. 52:1-52:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{suresh_et_al:LIPIcs.FSTTCS.2025.52,
  author =	{Suresh, Amrita and Yoshida, Nobuko},
  title =	{{Unreliability in Practical Subclasses of Communicating Systems}},
  booktitle =	{45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)},
  pages =	{52:1--52:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-406-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{360},
  editor =	{Aiswarya, C. and Mehta, Ruta and Roy, Subhajit},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2025.52},
  URN =		{urn:nbn:de:0030-drops-251312},
  doi =		{10.4230/LIPIcs.FSTTCS.2025.52},
  annote =	{Keywords: Communicating automata, lossy channel, corruption, out of order, session types, crash-stop failure}
}

Document

DOI: 10.4230/LIPIcs.ITP.2025.15

Certified Implementability of Global Multiparty Protocols

Authors: Elaine Li and Thomas Wies

Published in: LIPIcs, Volume 352, 16th International Conference on Interactive Theorem Proving (ITP 2025)

Abstract

Implementability is the decision problem at the heart of top-down approaches to protocol verification. In this paper, we present a mechanization of a recently proposed precise implementability characterization by Li et al. for a large class of protocols that subsumes many existing formalisms in the literature. Our protocols and implementations model asynchronous commmunication, and can exhibit infinite behavior. We improve upon their pen-and-paper results by unifying distinct formalisms, simplifying existing proof arguments, elaborating on the construction of canonical implementations, and even uncovering a subtle bug in the semantics for infinite words. As a corollary of our mechanization, we show that the original characterization of implementability applies even to protocols with infinitely many participants. We also contribute a reusable library for reasoning about generic communicating state machines. Our mechanization consists of about 15k lines of Rocq code. We believe that our mechanization can provide the foundation for deductively proving the implementability of protocols beyond the reach of prior work, extracting certified implementations for finite protocols, and investigating implementability under alternative asynchronous communication models.

Cite as

Elaine Li and Thomas Wies. Certified Implementability of Global Multiparty Protocols. In 16th International Conference on Interactive Theorem Proving (ITP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 352, pp. 15:1-15:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{li_et_al:LIPIcs.ITP.2025.15,
  author =	{Li, Elaine and Wies, Thomas},
  title =	{{Certified Implementability of Global Multiparty Protocols}},
  booktitle =	{16th International Conference on Interactive Theorem Proving (ITP 2025)},
  pages =	{15:1--15:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-396-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{352},
  editor =	{Forster, Yannick and Keller, Chantal},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2025.15},
  URN =		{urn:nbn:de:0030-drops-246139},
  doi =		{10.4230/LIPIcs.ITP.2025.15},
  annote =	{Keywords: Asynchronous protocols, communicating state machines, labeled transition systems, infinite semantics, realizability, multiparty session types, choreographies, deadlock freedom}
}

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Invited Talk

DOI: 10.4230/LIPIcs.MFCS.2025.5

On Synthesis of Distributed Monitors (Invited Talk)

Authors: Anca Muscholl

Published in: LIPIcs, Volume 345, 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)

Abstract

This talk addresses the synthesis problem of distributed monitors for concurrency properties.

Cite as

Anca Muscholl. On Synthesis of Distributed Monitors (Invited Talk). In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 5:1-5:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{muscholl:LIPIcs.MFCS.2025.5,
  author =	{Muscholl, Anca},
  title =	{{On Synthesis of Distributed Monitors}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{5:1--5:3},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-388-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{345},
  editor =	{Gawrychowski, Pawe{\l} and Mazowiecki, Filip and Skrzypczak, Micha{\l}},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2025.5},
  URN =		{urn:nbn:de:0030-drops-241126},
  doi =		{10.4230/LIPIcs.MFCS.2025.5},
  annote =	{Keywords: Distributed synthesis, monitoring}
}

Document

DOI: 10.4230/LIPIcs.MFCS.2025.79

Deciding Robust Instances of an Escape Problem for Dynamical Systems in Euclidean Space

Authors: Eike Neumann

Published in: LIPIcs, Volume 345, 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)

Abstract

We study the problem of deciding whether a point escapes a closed subset of ℝ^d under the iteration of a continuous map f : ℝ^d → ℝ^d in the bit-model of real computation. We give a sound partial decision method for this problem which is complete in the sense that its halting set contains the halting set of all sound partial decision methods for the problem. Equivalently, our decision method terminates on all problem instances whose answer is robust under all sufficiently small perturbations of the function. We further show that the halting set of our algorithm is dense in the set of all problem instances. While our algorithm applies to general continuous functions, we demonstrate that it also yields complete decision methods for much more rigid function families: affine linear systems and quadratic complex polynomials. In the latter case, completeness is subject to the density of hyperbolicity conjecture in complex dynamics. This in particular yields an alternative proof of Hertling’s (2004) conditional answer to a question raised by Penrose (1989) regarding the computability of the Mandelbrot set.

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Eike Neumann. Deciding Robust Instances of an Escape Problem for Dynamical Systems in Euclidean Space. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 79:1-79:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{neumann:LIPIcs.MFCS.2025.79,
  author =	{Neumann, Eike},
  title =	{{Deciding Robust Instances of an Escape Problem for Dynamical Systems in Euclidean Space}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{79:1--79:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-388-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{345},
  editor =	{Gawrychowski, Pawe{\l} and Mazowiecki, Filip and Skrzypczak, Micha{\l}},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2025.79},
  URN =		{urn:nbn:de:0030-drops-241866},
  doi =		{10.4230/LIPIcs.MFCS.2025.79},
  annote =	{Keywords: Dynamical Systems, Computability in Analysis, Non-Linear Functions}
}

Document

DOI: 10.4230/LIPIcs.CONCUR.2025.15

On the Send-Synchronizability Problem for Mailbox Communication

Authors: Romain Delpy, Anca Muscholl, and Grégoire Sutre

Published in: LIPIcs, Volume 348, 36th International Conference on Concurrency Theory (CONCUR 2025)

Abstract

A system of communicating automata is send-synchronizable if its set of send sequences (i.e., the projection on send actions of its executions) is the same when communications are asynchronous and when they are rendez-vous synchronizations. Send-synchronizability was claimed to be decidable for the mailbox semantics (Basu and Bultan, 2011) and for the peer-to-peer semantics (Basu and Bultan, 2016). Finkel and Lozes showed in 2017 that the proofs of these results are flawed, and they proved that send-synchronizability is in fact undecidable for peer-to-peer systems. The send-synchronizability problem for mailbox systems was left open. A partial solution was recently proposed in (Di Giusto, Laversa and Peters, 2024). In this paper, we revisit the send-synchronizability problem for mailbox systems. Firstly, we show that send-synchronizability is undecidable for mailbox systems, thus closing the question left open in (Finkel and Lozes, 2023) and (Di Giusto, Laversa and Peters, 2024). Secondly, we show that send-synchronizability is decidable for the class of 1-schedulable mailbox systems. A system is 1-schedulable if every execution can be re-scheduled into an equivalent execution where each send is either immediately followed by its matching receive, or is never matched. Despite the apparent similarity between send-synchronizability and 1-schedulability, the proof that send-synchronizability is decidable for 1-schedulable mailbox systems is quite involved. We believe that the techniques that we develop in this proof could be used to address other problems on mailbox systems, such as the realizability problem.

Cite as

Romain Delpy, Anca Muscholl, and Grégoire Sutre. On the Send-Synchronizability Problem for Mailbox Communication. In 36th International Conference on Concurrency Theory (CONCUR 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 348, pp. 15:1-15:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{delpy_et_al:LIPIcs.CONCUR.2025.15,
  author =	{Delpy, Romain and Muscholl, Anca and Sutre, Gr\'{e}goire},
  title =	{{On the Send-Synchronizability Problem for Mailbox Communication}},
  booktitle =	{36th International Conference on Concurrency Theory (CONCUR 2025)},
  pages =	{15:1--15:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-389-8},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{348},
  editor =	{Bouyer, Patricia and van de Pol, Jaco},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2025.15},
  URN =		{urn:nbn:de:0030-drops-239659},
  doi =		{10.4230/LIPIcs.CONCUR.2025.15},
  annote =	{Keywords: Concurrent programming, Mailbox communication, Verification, Synchronizability}
}

Document

DOI: 10.4230/LIPIcs.CONCUR.2025.6

Omega-Regular Verification and Control for Distributional Specifications in MDPs

Authors: S. Akshay, Ouldouz Neysari, and Ðorđe Žikelić

Published in: LIPIcs, Volume 348, 36th International Conference on Concurrency Theory (CONCUR 2025)

Abstract

A classical approach to studying Markov decision processes (MDPs) is to view them as state transformers. However, MDPs can also be viewed as distribution transformers, where an MDP under a strategy generates a sequence of probability distributions over MDP states. This view arises in several applications, even as the probabilistic model checking problem becomes much harder compared to the classical state transformer counterpart. It is known that even distributional reachability and safety problems become computationally intractable (Skolem- and positivity-hard). To address this challenge, recent works focused on sound but possibly incomplete methods for verification and control of MDPs under the distributional view. However, existing automated methods are applicable only to distributional reachability, safety and reach-avoidance specifications. In this work, we present the first automated method for verification and control of MDPs with respect to distributional omega-regular specifications. To achieve this, we propose a novel notion of distributional certificates, which are sound and complete proof rules for proving that an MDP under a distributionally memoryless strategy satisfies some distributional omega-regular specification. We then use our distributional certificates to design the first fully automated algorithms for verification and control of MDPs with respect to distributional omega-regular specifications. Our algorithms follow a template-based synthesis approach and provide soundness and relative completeness guarantees, while running in PSPACE. Our prototype implementation demonstrates practical applicability of our algorithms to challenging examples collected from the literature.

Cite as

S. Akshay, Ouldouz Neysari, and Ðorđe Žikelić. Omega-Regular Verification and Control for Distributional Specifications in MDPs. In 36th International Conference on Concurrency Theory (CONCUR 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 348, pp. 6:1-6:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{akshay_et_al:LIPIcs.CONCUR.2025.6,
  author =	{Akshay, S. and Neysari, Ouldouz and \v{Z}ikeli\'{c}, Ðor{\d}e},
  title =	{{Omega-Regular Verification and Control for Distributional Specifications in MDPs}},
  booktitle =	{36th International Conference on Concurrency Theory (CONCUR 2025)},
  pages =	{6:1--6:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-389-8},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{348},
  editor =	{Bouyer, Patricia and van de Pol, Jaco},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2025.6},
  URN =		{urn:nbn:de:0030-drops-239562},
  doi =		{10.4230/LIPIcs.CONCUR.2025.6},
  annote =	{Keywords: MDPs, Distributional objectives, \omega-regularity, Certificates}
}

Document

DOI: 10.4230/LIPIcs.FSCD.2025.31

Higher-Dimensional Automata: Extension to Infinite Tracks

Authors: Luc Passemard, Amazigh Amrane, and Uli Fahrenberg

Published in: LIPIcs, Volume 337, 10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025)

Abstract

We introduce higher-dimensional automata for infinite interval ipomsets (ω-HDAs). We define key concepts from different points of view, inspired from their finite counterparts. Then we explore languages recognized by ω-HDAs under Büchi and Muller semantics. We show that Muller acceptance is more expressive than Büchi acceptance and, in contrast to the finite case, both semantics do not yield languages closed under subsumption. Then, we adapt the original rational operations to deal with ω-HDAs and show that while languages of ω-HDAs are ω-rational, not all ω-rational languages can be expressed by ω-HDAs.

Cite as

Luc Passemard, Amazigh Amrane, and Uli Fahrenberg. Higher-Dimensional Automata: Extension to Infinite Tracks. In 10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 337, pp. 31:1-31:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{passemard_et_al:LIPIcs.FSCD.2025.31,
  author =	{Passemard, Luc and Amrane, Amazigh and Fahrenberg, Uli},
  title =	{{Higher-Dimensional Automata: Extension to Infinite Tracks}},
  booktitle =	{10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025)},
  pages =	{31:1--31:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-374-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{337},
  editor =	{Fern\'{a}ndez, Maribel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2025.31},
  URN =		{urn:nbn:de:0030-drops-236466},
  doi =		{10.4230/LIPIcs.FSCD.2025.31},
  annote =	{Keywords: Higher-dimensional automata, concurrency theory, omega pomsets, B\"{u}chi acceptance, Muller acceptance, interval pomsets, pomsets with interfaces}
}

Document

Track B: Automata, Logic, Semantics, and Theory of Programming

DOI: 10.4230/LIPIcs.ICALP.2025.163

Verification of Linear Dynamical Systems via O-Minimality of the Real Numbers

Authors: Toghrul Karimov

Published in: LIPIcs, Volume 334, 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)

Abstract

A discrete-time linear dynamical system (LDS) is given by an update matrix M ∈ ℝ^{d× d}, and has the trajectories ⟨s, Ms, M²s, …⟩ for s ∈ ℝ^d. Reachability-type decision problems of linear dynamical systems, most notably the Skolem Problem, lie at the forefront of decidability: typically, sound and complete algorithms are known only in low dimensions, and these rely on sophisticated tools from number theory and Diophantine approximation. Recently, however, o-minimality has emerged as a counterpoint to these number-theoretic tools that allows us to decide certain modifications of the classical problems of LDS without any dimension restrictions. In this paper, we first introduce the Decomposition Method, a framework that captures all applications of o-minimality to decision problems of LDS that are currently known to us. We then use the Decomposition Method to show decidability of the Robust Safety Problem (restricted to bounded initial sets) in arbitrary dimension: given a matrix M, a bounded semialgebraic set S of initial points, and a semialgebraic set T of unsafe points, it is decidable whether there exists ε > 0 such that all orbits that begin in the ε-ball around S avoid T.

Cite as

Toghrul Karimov. Verification of Linear Dynamical Systems via O-Minimality of the Real Numbers. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 163:1-163:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{karimov:LIPIcs.ICALP.2025.163,
  author =	{Karimov, Toghrul},
  title =	{{Verification of Linear Dynamical Systems via O-Minimality of the Real Numbers}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{163:1--163:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-372-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{334},
  editor =	{Censor-Hillel, Keren and Grandoni, Fabrizio and Ouaknine, Jo\"{e}l and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2025.163},
  URN =		{urn:nbn:de:0030-drops-235401},
  doi =		{10.4230/LIPIcs.ICALP.2025.163},
  annote =	{Keywords: Linear dynamical systems, reachability problems, o-minimality}
}

Document

DOI: 10.4230/LIPIcs.FSTTCS.2023.13

Reinforcement Planning for Effective ε-Optimal Policies in Dense Time with Discontinuities

Authors: Léo Henry, Blaise Genest, and Alexandre Drewery

Published in: LIPIcs, Volume 284, 43rd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2023)

Abstract

Lately, the model of (Decision) Stochastic Timed Automata (DSTA) has been proposed, to model those Cyber Physical Systems displaying dense time (physical part), discrete actions and discontinuities such as timeouts (cyber part). The state of the art results on controlling DSTAs are however not ideal: in the case of infinite horizon, optimal controllers do not exist, while for timed bounded behaviors, we do not know how to build such controllers, even ε-optimal ones. In this paper, we develop a theory of Reinforcement Planning in the setting of DSTAs, for discounted infinite horizon objectives. We show that optimal controllers do exist in general. Further, for DSTAs with 1 clock (which already generalize Continuous Time MDPs with e.g. timeouts), we provide an effective procedure to compute ε-optimal controllers. It is worth noting that we do not rely on the discretization of the time space, but consider symbolic representations instead. Evaluation on a DSTA shows that this method can be more efficient. Last, we show on a counterexample that this is the furthest this construction can go, as it cannot be extended to 2 or more clocks.

Cite as

Léo Henry, Blaise Genest, and Alexandre Drewery. Reinforcement Planning for Effective ε-Optimal Policies in Dense Time with Discontinuities. In 43rd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 284, pp. 13:1-13:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{henry_et_al:LIPIcs.FSTTCS.2023.13,
  author =	{Henry, L\'{e}o and Genest, Blaise and Drewery, Alexandre},
  title =	{{Reinforcement Planning for Effective \epsilon-Optimal Policies in Dense Time with Discontinuities}},
  booktitle =	{43rd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2023)},
  pages =	{13:1--13:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-304-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{284},
  editor =	{Bouyer, Patricia and Srinivasan, Srikanth},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2023.13},
  URN =		{urn:nbn:de:0030-drops-193866},
  doi =		{10.4230/LIPIcs.FSTTCS.2023.13},
  annote =	{Keywords: reinforcement planning, timed automata, planning}
}

Document

DOI: 10.4230/LIPIcs.FSTTCS.2023.17

Robust Positivity Problems for Linear Recurrence Sequences: The Frontiers of Decidability for Explicitly Given Neighbourhoods

Authors: Mihir Vahanwala

Published in: LIPIcs, Volume 284, 43rd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2023)

Abstract

Linear Recurrence Sequences (LRS) are a fundamental mathematical primitive for a plethora of applications such as the verification of probabilistic systems, model checking, computational biology, and economics. Positivity (are all terms of the given LRS non-negative?) and Ultimate Positivity (are all but finitely many terms of the given LRS non-negative?) are important open number-theoretic decision problems. Recently, the robust versions of these problems, that ask whether the LRS is (Ultimately) Positive despite small perturbations to its initialisation, have gained attention as a means to model the imprecision that arises in practical settings. However, the state of the art is ill-equipped to reason about imprecision when its extent is explicitly specified. In this paper, we consider Robust Positivity and Ultimate Positivity problems where the neighbourhood of the initialisation, expressed in a natural and general format, is also part of the input. We contribute by proving sharp decidability results: decision procedures at orders our techniques are unable to handle for general LRS would entail significant number-theoretic breakthroughs.

Cite as

Mihir Vahanwala. Robust Positivity Problems for Linear Recurrence Sequences: The Frontiers of Decidability for Explicitly Given Neighbourhoods. In 43rd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 284, pp. 17:1-17:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{vahanwala:LIPIcs.FSTTCS.2023.17,
  author =	{Vahanwala, Mihir},
  title =	{{Robust Positivity Problems for Linear Recurrence Sequences: The Frontiers of Decidability for Explicitly Given Neighbourhoods}},
  booktitle =	{43rd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2023)},
  pages =	{17:1--17:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-304-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{284},
  editor =	{Bouyer, Patricia and Srinivasan, Srikanth},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2023.17},
  URN =		{urn:nbn:de:0030-drops-193909},
  doi =		{10.4230/LIPIcs.FSTTCS.2023.17},
  annote =	{Keywords: Dynamical Systems, Verification, Robustness, Linear Recurrence Sequences, Positivity, Ultimate Positivity}
}

Document

DOI: 10.4230/LIPIcs.STACS.2022.5

On Robustness for the Skolem and Positivity Problems

Authors: S. Akshay, Hugo Bazille, Blaise Genest, and Mihir Vahanwala

Published in: LIPIcs, Volume 219, 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)

Abstract

The Skolem problem is a long-standing open problem in linear dynamical systems: can a linear recurrence sequence (LRS) ever reach 0 from a given initial configuration? Similarly, the positivity problem asks whether the LRS stays positive from an initial configuration. Deciding Skolem (or positivity) has been open for half a century: The best known decidability results are for LRS with special properties (e.g., low order recurrences). On the other hand, these problems are much easier for "uninitialized" variants, where the initial configuration is not fixed but can vary arbitrarily: checking if there is an initial configuration from which the LRS stays positive can be decided by polynomial time algorithms (Tiwari in 2004, Braverman in 2006). In this paper, we consider problems that lie between the initialized and uninitialized variant. More precisely, we ask if 0 (resp. negative numbers) can be avoided from every initial configuration in a neighborhood of a given initial configuration. This can be considered as a robust variant of the Skolem (resp. positivity) problem. We show that these problems lie at the frontier of decidability: if the neighborhood is given as part of the input, then robust Skolem and robust positivity are Diophantine-hard, i.e., solving either would entail major breakthrough in Diophantine approximations, as happens for (non-robust) positivity. Interestingly, this is the first Diophantine-hardness result on a variant of the Skolem problem, to the best of our knowledge. On the other hand, if one asks whether such a neighborhood exists, then the problems turn out to be decidable in their full generality, with PSPACE complexity. Our analysis is based on the set of initial configurations such that positivity holds, which leads to new insights into these difficult problems, and interesting geometrical interpretations.

Cite as

S. Akshay, Hugo Bazille, Blaise Genest, and Mihir Vahanwala. On Robustness for the Skolem and Positivity Problems. In 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 219, pp. 5:1-5:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{akshay_et_al:LIPIcs.STACS.2022.5,
  author =	{Akshay, S. and Bazille, Hugo and Genest, Blaise and Vahanwala, Mihir},
  title =	{{On Robustness for the Skolem and Positivity Problems}},
  booktitle =	{39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)},
  pages =	{5:1--5:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-222-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{219},
  editor =	{Berenbrink, Petra and Monmege, Benjamin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2022.5},
  URN =		{urn:nbn:de:0030-drops-158156},
  doi =		{10.4230/LIPIcs.STACS.2022.5},
  annote =	{Keywords: Skolem problem, verification, dynamical systems, robustness}
}

Document

Invited Talk

DOI: 10.4230/LIPIcs.FSTTCS.2021.2

State Complexity of Population Protocols (Invited Talk)

Authors: Javier Esparza

Published in: LIPIcs, Volume 213, 41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021)

Abstract

Population protocols were introduced by Angluin et al. in 2004 to study the theoretical properties of networks of mobile sensors with very limited computational resources. They have also been proposed as a natural computing model, with molecules, cells, or microorganisms playing the role of sensors. In a population protocol an arbitrary number of indistinguishable, finite-state agents interact randomly in pairs to collectively decide if their initial global configuration satisfies a given property. The property is formalized as a predicate that maps each initial configuration to an output, 0 or 1. Starting from an initial configuration, the agents eventually agree to the correct output almost surely, and continue producing it forever. The protocol is said to stabilize to the correct output. It is well known that population protocols can decide exactly the semilinear predicates, or, equivalently, the predicates expressible in Presburger arithmetic. Current research concentrates on investigating the amount of resources needed to decide a given predicate. The standard resources, time and memory, translate for population protocols into expected time to stabilization, usually called parallel runtime, and number of states of each agent. In this talk we concentrate on the latter. A variant of population protocols allows for a leader, a distinguished finite-state agent that is added to the initial configuration and, intuitively, helps the other agents to organize the computation. In the last years my collaborators and I have obtained upper and lower bounds for the state complexity of population protocols with and without a leader. Define the state complexity of a predicate as the minimal number of states of a protocol that decides the predicate, and STATE(η) as the maximum state complexity of the predicates of size at most η, where predicates are encoded as quantifier-free formulas of Presburger arithmetic with coefficients written in binary. Using techniques from the theory of Petri nets and Vector Addition Systems, we have shown that STATE(η) is polynomially bounded, even for leaderless protocols; this improves on the exponential bound given in 2004 by Angluin and collaborators. We have also proved that STATE(η) ∈ Ω(log log η) for leaderless protocols, even for those deciding very simple predicates of the form x ≥ c for some constant c. In the talk I report on these results, and on two very recent, still unpublished results. Modulo the pending peer-review confirmation, the first result shows the existence of leaderless protocols with a polynomial number of states and linear parallel runtime, and the second, due to Leroux, gives a Ω((log log η)^{1/3}) lower bound for protocols with a leader.

Cite as

Javier Esparza. State Complexity of Population Protocols (Invited Talk). In 41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 213, p. 2:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{esparza:LIPIcs.FSTTCS.2021.2,
  author =	{Esparza, Javier},
  title =	{{State Complexity of Population Protocols}},
  booktitle =	{41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021)},
  pages =	{2:1--2:1},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-215-0},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{213},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Chekuri, Chandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2021.2},
  URN =		{urn:nbn:de:0030-drops-155139},
  doi =		{10.4230/LIPIcs.FSTTCS.2021.2},
  annote =	{Keywords: Population protocols, state complexity, Petri nets}
}

Document

DOI: 10.4230/LIPIcs.FSTTCS.2021.33

Resilience of Timed Systems

Authors: S. Akshay, Blaise Genest, Loïc Hélouët, S. Krishna, and Sparsa Roychowdhury

Published in: LIPIcs, Volume 213, 41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021)

Abstract

This paper addresses reliability of timed systems in the setting of resilience, that considers the behaviors of a system when unspecified timing errors such as missed deadlines occur. Given a fault model that allows transitions to fire later than allowed by their guard, a system is universally resilient (or self-resilient) if after a fault, it always returns to a timed behavior of the non-faulty system. It is existentially resilient if after a fault, there exists a way to return to a timed behavior of the non-faulty system, that is, if there exists a controller which can guide the system back to a normal behavior. We show that universal resilience of timed automata is undecidable, while existential resilience is decidable, in EXPSPACE. To obtain better complexity bounds and decidability of universal resilience, we consider untimed resilience, as well as subclasses of timed automata.

Cite as

S. Akshay, Blaise Genest, Loïc Hélouët, S. Krishna, and Sparsa Roychowdhury. Resilience of Timed Systems. In 41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 213, pp. 33:1-33:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{akshay_et_al:LIPIcs.FSTTCS.2021.33,
  author =	{Akshay, S. and Genest, Blaise and H\'{e}lou\"{e}t, Lo\"{i}c and Krishna, S. and Roychowdhury, Sparsa},
  title =	{{Resilience of Timed Systems}},
  booktitle =	{41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021)},
  pages =	{33:1--33:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-215-0},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{213},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Chekuri, Chandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2021.33},
  URN =		{urn:nbn:de:0030-drops-155442},
  doi =		{10.4230/LIPIcs.FSTTCS.2021.33},
  annote =	{Keywords: Timed automata, Fault tolerance, Integer-resets, Resilience}
}

Document

DOI: 10.4230/LIPIcs.STACS.2020.40

Succinct Population Protocols for Presburger Arithmetic

Authors: Michael Blondin, Javier Esparza, Blaise Genest, Martin Helfrich, and Stefan Jaax

Published in: LIPIcs, Volume 154, 37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020)

Abstract

In [Dana Angluin et al., 2006], Angluin et al. proved that population protocols compute exactly the predicates definable in Presburger arithmetic (PA), the first-order theory of addition. As part of this result, they presented a procedure that translates any formula φ of quantifier-free PA with remainder predicates (which has the same expressive power as full PA) into a population protocol with 2^?(poly(|φ|)) states that computes φ. More precisely, the number of states of the protocol is exponential in both the bit length of the largest coefficient in the formula, and the number of nodes of its syntax tree. In this paper, we prove that every formula φ of quantifier-free PA with remainder predicates is computable by a leaderless population protocol with ?(poly(|φ|)) states. Our proof is based on several new constructions, which may be of independent interest. Given a formula φ of quantifier-free PA with remainder predicates, a first construction produces a succinct protocol (with ?(|φ|³) leaders) that computes φ; this completes the work initiated in [Michael Blondin et al., 2018], where we constructed such protocols for a fragment of PA. For large enough inputs, we can get rid of these leaders. If the input is not large enough, then it is small, and we design another construction producing a succinct protocol with one leader that computes φ. Our last construction gets rid of this leader for small inputs.

Cite as

Michael Blondin, Javier Esparza, Blaise Genest, Martin Helfrich, and Stefan Jaax. Succinct Population Protocols for Presburger Arithmetic. In 37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 154, pp. 40:1-40:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{blondin_et_al:LIPIcs.STACS.2020.40,
  author =	{Blondin, Michael and Esparza, Javier and Genest, Blaise and Helfrich, Martin and Jaax, Stefan},
  title =	{{Succinct Population Protocols for Presburger Arithmetic}},
  booktitle =	{37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020)},
  pages =	{40:1--40:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-140-5},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{154},
  editor =	{Paul, Christophe and Bl\"{a}ser, Markus},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2020.40},
  URN =		{urn:nbn:de:0030-drops-119018},
  doi =		{10.4230/LIPIcs.STACS.2020.40},
  annote =	{Keywords: Population protocols, Presburger arithmetic, state complexity}
}

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