22 Search Results for "Leroux, Jérôme"

Volume

LIPIcs, Volume 272

48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)

MFCS 2023, August 28 to September 1, 2023, Bordeaux, France

Editors: Jérôme Leroux, Sylvain Lombardy, and David Peleg

Document
DOI: 10.4230/LIPIcs.ITP.2024.30
A Coq Formalization of Taylor Models and Power Series for Solving Ordinary Differential Equations

Authors: Sewon Park and Holger Thies

Published in: LIPIcs, Volume 309, 15th International Conference on Interactive Theorem Proving (ITP 2024)

Abstract
In exact real computation real numbers are manipulated exactly without round-off errors, making it well-suited for high precision verified computation. In recent work we propose an axiomatic formalization of exact real computation in the Coq theorem prover. The formalization admits an extended extraction mechanism that lets us extract computational content from constructive parts of proofs to efficient programs built on top of AERN, a Haskell library for exact real computation. Many processes in science and engineering are modeled by ordinary differential equations (ODEs), and often safety-critical applications depend on computing their solutions correctly. The primary goal of the current work is to extend our framework to spaces of functions and to support computation of solutions to ODEs and other essential operators. In numerical mathematics, the most common way to represent continuous functions is to use polynomial approximations. This can be modeled by so-called Taylor models, that encode a function as a polynomial and a rigorous error-bound over some domain. We define types of classical functions that do not hold any computational content and formalize Taylor models to computationally approximate those classical functions. Classical functions are defined in a way to admit classical principles in their constructions and verification. We define various basic operations on Taylor models and verify their correctness based on the classical functions that they approximate. We then shift our interest to analytic functions as a generalization of Taylor models where polynomials are replaced by infinite power series. We use the formalization to develop a theory of non-linear polynomial ODEs. From the proofs we can extract certified exact real computation programs that compute solutions of ODEs on some time interval up to any precision.
Cite as

Sewon Park and Holger Thies. A Coq Formalization of Taylor Models and Power Series for Solving Ordinary Differential Equations. In 15th International Conference on Interactive Theorem Proving (ITP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 309, pp. 30:1-30:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{park_et_al:LIPIcs.ITP.2024.30,
  author =	{Park, Sewon and Thies, Holger},
  title =	{{A Coq Formalization of Taylor Models and Power Series for Solving Ordinary Differential Equations}},
  booktitle =	{15th International Conference on Interactive Theorem Proving (ITP 2024)},
  pages =	{30:1--30:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-337-9},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{309},
  editor =	{Bertot, Yves and Kutsia, Temur and Norrish, Michael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2024.30},
  URN =		{urn:nbn:de:0030-drops-207581},
  doi =		{10.4230/LIPIcs.ITP.2024.30},
  annote =	{Keywords: Exact real computation, Taylor models, Analytic functions, Computable analysis, Program extraction}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2024.17
Invariants for One-Counter Automata with Disequality Tests

Authors: Dmitry Chistikov, Jérôme Leroux, Henry Sinclair-Banks, and Nicolas Waldburger

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

Abstract
We study the reachability problem for one-counter automata in which transitions can carry disequality tests. A disequality test is a guard that prohibits a specified counter value. This reachability problem has been known to be NP-hard and in PSPACE, and characterising its computational complexity has been left as a challenging open question by Almagor, Cohen, Pérez, Shirmohammadi, and Worrell (2020). We reduce the complexity gap, placing the problem into the second level of the polynomial hierarchy, namely into the class coNP^NP. In the presence of both equality and disequality tests, our upper bound is at the third level, P^NP^NP. To prove this result, we show that non-reachability can be witnessed by a pair of invariants (forward and backward). These invariants are almost inductive. They aim to over-approximate only a "core" of the reachability set instead of the entire set. The invariants are also leaky: it is possible to escape the set. We complement this with separate checks as the leaks can only occur in a controlled way.
Cite as

Dmitry Chistikov, Jérôme Leroux, Henry Sinclair-Banks, and Nicolas Waldburger. Invariants for One-Counter Automata with Disequality Tests. In 35th International Conference on Concurrency Theory (CONCUR 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 311, pp. 17:1-17:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{chistikov_et_al:LIPIcs.CONCUR.2024.17,
  author =	{Chistikov, Dmitry and Leroux, J\'{e}r\^{o}me and Sinclair-Banks, Henry and Waldburger, Nicolas},
  title =	{{Invariants for One-Counter Automata with Disequality Tests}},
  booktitle =	{35th International Conference on Concurrency Theory (CONCUR 2024)},
  pages =	{17:1--17:21},
  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.2024.17},
  URN =		{urn:nbn:de:0030-drops-207898},
  doi =		{10.4230/LIPIcs.CONCUR.2024.17},
  annote =	{Keywords: Inductive invariant, Vector addition system, One-counter automaton}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2024.141
Flattability of Priority Vector Addition Systems

Authors: Roland Guttenberg

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

Abstract
Vector addition systems (VAS), also known as Petri nets, are a popular model of concurrent systems. Many problems from many areas reduce to the reachability problem for VAS, which consists of deciding whether a target configuration of a VAS is reachable from a given initial configuration. One of the main approaches to solve the problem on practical instances is called flattening, intuitively removing nested loops. This technique is known to terminate for semilinear VAS due to [Jérôme Leroux, 2013]. In this paper, we prove that also for VAS with nested zero tests, called Priority VAS, flattening does in fact terminate for all semilinear reachability relations. Furthermore, we prove that Priority VAS admit semilinear inductive invariants. Both of these results are obtained by defining a well-quasi-order on runs of Priority VAS which has good pumping properties.
Cite as

Roland Guttenberg. Flattability of Priority Vector Addition Systems. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 141:1-141:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{guttenberg:LIPIcs.ICALP.2024.141,
  author =	{Guttenberg, Roland},
  title =	{{Flattability of Priority Vector Addition Systems}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{141:1--141:20},
  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.2024.141},
  URN =		{urn:nbn:de:0030-drops-202848},
  doi =		{10.4230/LIPIcs.ICALP.2024.141},
  annote =	{Keywords: Priority Vector Addition Systems, Semilinear, Inductive Invariants, Geometry, Flattability, Almost Semilinear, Transformer Relation}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2023.35
New Lower Bounds for Reachability in Vector Addition Systems

Authors: Wojciech Czerwiński, Ismaël Jecker, Sławomir Lasota, Jérôme Leroux, and Łukasz Orlikowski

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

Abstract
We investigate the dimension-parametric complexity of the reachability problem in vector addition systems with states (VASS) and its extension with pushdown stack (pushdown VASS). Up to now, the problem is known to be F_d-hard for VASS of dimension 3d+2 (the complexity class F_d corresponds to the kth level of the fast-growing hierarchy), and no essentially better bound is known for pushdown VASS. We provide a new construction that improves the lower bound for VASS: F_d-hardness in dimension 2d+3. Furthermore, building on our new insights we show a new lower bound for pushdown VASS: F_d-hardness in dimension d/2 + 6. This dimension-parametric lower bound is strictly stronger than the upper bound for VASS, which suggests that the (still unknown) complexity of the reachability problem in pushdown VASS is higher than in plain VASS (where it is Ackermann-complete).
Cite as

Wojciech Czerwiński, Ismaël Jecker, Sławomir Lasota, Jérôme Leroux, and Łukasz Orlikowski. New Lower Bounds for Reachability in Vector Addition Systems. 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. 35:1-35:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{czerwinski_et_al:LIPIcs.FSTTCS.2023.35,
  author =	{Czerwi\'{n}ski, Wojciech and Jecker, Isma\"{e}l and Lasota, S{\l}awomir and Leroux, J\'{e}r\^{o}me and Orlikowski, {\L}ukasz},
  title =	{{New Lower Bounds for Reachability in Vector Addition Systems}},
  booktitle =	{43rd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2023)},
  pages =	{35:1--35:22},
  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.2023.35},
  URN =		{urn:nbn:de:0030-drops-194088},
  doi =		{10.4230/LIPIcs.FSTTCS.2023.35},
  annote =	{Keywords: vector addition systems, reachability problem, pushdown vector addition system, lower bounds}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2023.36
The Semilinear Home-Space Problem Is Ackermann-Complete for Petri Nets

Authors: Petr Jančar and Jérôme Leroux

Published in: LIPIcs, Volume 279, 34th International Conference on Concurrency Theory (CONCUR 2023)

Abstract
A set of configurations H is a home-space for a set of configurations X of a Petri net if every configuration reachable from (any configuration in) X can reach (some configuration in) H. The semilinear home-space problem for Petri nets asks, given a Petri net and semilinear sets of configurations X, H, if H is a home-space for X. In 1989, David de Frutos Escrig and Colette Johnen proved that the problem is decidable when X is a singleton and H is a finite union of linear sets with the same periods. In this paper, we show that the general (semilinear) problem is decidable. This result is obtained by proving a duality between the reachability problem and the non-home-space problem. In particular, we prove that for any Petri net and any linear set of configurations L we can effectively compute a semilinear set C of configurations, called a non-reachability core for L, such that for every set X the set L is not a home-space for X if, and only if, C is reachable from X. We show that the established relation to the reachability problem yields the Ackermann-completeness of the (semilinear) home-space problem. For this we also show that, given a Petri net with an initial marking, the set of minimal reachable markings can be constructed in Ackermannian time.
Cite as

Petr Jančar and Jérôme Leroux. The Semilinear Home-Space Problem Is Ackermann-Complete for Petri Nets. In 34th International Conference on Concurrency Theory (CONCUR 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 279, pp. 36:1-36:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{jancar_et_al:LIPIcs.CONCUR.2023.36,
  author =	{Jan\v{c}ar, Petr and Leroux, J\'{e}r\^{o}me},
  title =	{{The Semilinear Home-Space Problem Is Ackermann-Complete for Petri Nets}},
  booktitle =	{34th International Conference on Concurrency Theory (CONCUR 2023)},
  pages =	{36:1--36:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-299-0},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{279},
  editor =	{P\'{e}rez, Guillermo A. and Raskin, Jean-Fran\c{c}ois},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2023.36},
  URN =		{urn:nbn:de:0030-drops-190300},
  doi =		{10.4230/LIPIcs.CONCUR.2023.36},
  annote =	{Keywords: Petri nets, home-space property, semilinear sets, Ackermannian complexity}
}
Document
Complete Volume
DOI: 10.4230/LIPIcs.MFCS.2023
LIPIcs, Volume 272, MFCS 2023, Complete Volume

Authors: Jérôme Leroux, Sylvain Lombardy, and David Peleg

Published in: LIPIcs, Volume 272, 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)

Abstract
LIPIcs, Volume 272, MFCS 2023, Complete Volume
Cite as

48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 1-1302, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@Proceedings{leroux_et_al:LIPIcs.MFCS.2023,
  title =	{{LIPIcs, Volume 272, MFCS 2023, Complete Volume}},
  booktitle =	{48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
  pages =	{1--1302},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-292-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{272},
  editor =	{Leroux, J\'{e}r\^{o}me and Lombardy, Sylvain and Peleg, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2023},
  URN =		{urn:nbn:de:0030-drops-185332},
  doi =		{10.4230/LIPIcs.MFCS.2023},
  annote =	{Keywords: LIPIcs, Volume 272, MFCS 2023, Complete Volume}
}
Document
Front Matter
DOI: 10.4230/LIPIcs.MFCS.2023.0
Front Matter, Table of Contents, Preface, Conference Organization

Authors: Jérôme Leroux, Sylvain Lombardy, and David Peleg

Published in: LIPIcs, Volume 272, 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)

Abstract
Front Matter, Table of Contents, Preface, Conference Organization
Cite as

48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 0:i-0:xviii, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{leroux_et_al:LIPIcs.MFCS.2023.0,
  author =	{Leroux, J\'{e}r\^{o}me and Lombardy, Sylvain and Peleg, David},
  title =	{{Front Matter, Table of Contents, Preface, Conference Organization}},
  booktitle =	{48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
  pages =	{0:i--0:xviii},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-292-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{272},
  editor =	{Leroux, J\'{e}r\^{o}me and Lombardy, Sylvain and Peleg, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2023.0},
  URN =		{urn:nbn:de:0030-drops-185349},
  doi =		{10.4230/LIPIcs.MFCS.2023.0},
  annote =	{Keywords: Front Matter, Table of Contents, Preface, Conference Organization}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2020.37
Reachability in Two-Dimensional Vector Addition Systems with States: One Test Is for Free

Authors: Jérôme Leroux and Grégoire Sutre

Published in: LIPIcs, Volume 171, 31st International Conference on Concurrency Theory (CONCUR 2020)

Abstract
Vector addition system with states is an ubiquitous model of computation with extensive applications in computer science. The reachability problem for vector addition systems is central since many other problems reduce to that question. The problem is decidable and it was recently proved that the dimension of the vector addition system is an important parameter of the complexity. In fixed dimensions larger than two, the complexity is not known (with huge complexity gaps). In dimension two, the reachability problem was shown to be PSPACE-complete by Blondin et al. in 2015. We consider an extension of this model, called 2-TVASS, where the first counter can be tested for zero. This model naturally extends the classical model of one counter automata (OCA). We show that reachability is still solvable in polynomial space for 2-TVASS. As in the work Blondin et al., our approach relies on the existence of small reachability certificates obtained by concatenating polynomially many cycles.
Cite as

Jérôme Leroux and Grégoire Sutre. Reachability in Two-Dimensional Vector Addition Systems with States: One Test Is for Free. In 31st International Conference on Concurrency Theory (CONCUR 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 171, pp. 37:1-37:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{leroux_et_al:LIPIcs.CONCUR.2020.37,
  author =	{Leroux, J\'{e}r\^{o}me and Sutre, Gr\'{e}goire},
  title =	{{Reachability in Two-Dimensional Vector Addition Systems with States: One Test Is for Free}},
  booktitle =	{31st International Conference on Concurrency Theory (CONCUR 2020)},
  pages =	{37:1--37:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-160-3},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{171},
  editor =	{Konnov, Igor and Kov\'{a}cs, Laura},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2020.37},
  URN =		{urn:nbn:de:0030-drops-128498},
  doi =		{10.4230/LIPIcs.CONCUR.2020.37},
  annote =	{Keywords: Counter machine, Vector addition system, Reachability problem, Formal verification, Infinite-state system}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2020.45
Flatness and Complexity of Immediate Observation Petri Nets

Authors: Mikhail Raskin, Chana Weil-Kennedy, and Javier Esparza

Published in: LIPIcs, Volume 171, 31st International Conference on Concurrency Theory (CONCUR 2020)

Abstract
In a previous paper we introduced immediate observation (IO) Petri nets, a class of interest in the study of population protocols and enzymatic chemical networks. In the first part of this paper we show that IO nets are globally flat, and so their safety properties can be checked by efficient symbolic model checking tools using acceleration techniques, like FAST. In the second part we study Branching IO nets (BIO nets), whose transitions can create tokens. BIO nets extend both IO nets and communication-free nets, also called BPP nets, a widely studied class. We show that, while BIO nets are no longer globally flat, and their sets of reachable markings may be non-semilinear, they are still locally flat. As a consequence, the coverability and reachability problem for BIO nets, and even a certain set-parameterized version of them, are in PSPACE. This makes BIO nets the first natural net class with non-semilinear reachability relation for which the reachability problem is provably simpler than for general Petri nets.
Cite as

Mikhail Raskin, Chana Weil-Kennedy, and Javier Esparza. Flatness and Complexity of Immediate Observation Petri Nets. In 31st International Conference on Concurrency Theory (CONCUR 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 171, pp. 45:1-45:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{raskin_et_al:LIPIcs.CONCUR.2020.45,
  author =	{Raskin, Mikhail and Weil-Kennedy, Chana and Esparza, Javier},
  title =	{{Flatness and Complexity of Immediate Observation Petri Nets}},
  booktitle =	{31st International Conference on Concurrency Theory (CONCUR 2020)},
  pages =	{45:1--45:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-160-3},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{171},
  editor =	{Konnov, Igor and Kov\'{a}cs, Laura},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2020.45},
  URN =		{urn:nbn:de:0030-drops-128574},
  doi =		{10.4230/LIPIcs.CONCUR.2020.45},
  annote =	{Keywords: Petri Nets, Reachability Analysis, Parameterized Verification, Flattability}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2020.48
Reachability in Fixed Dimension Vector Addition Systems with States

Authors: Wojciech Czerwiński, Sławomir Lasota, Ranko Lazić, Jérôme Leroux, and Filip Mazowiecki

Published in: LIPIcs, Volume 171, 31st International Conference on Concurrency Theory (CONCUR 2020)

Abstract
The reachability problem is a central decision problem in verification of vector addition systems with states (VASS). In spite of recent progress, the complexity of the reachability problem remains unsettled, and it is closely related to the lengths of shortest VASS runs that witness reachability. We obtain three main results for VASS of fixed dimension. For the first two, we assume that the integers in the input are given in unary, and that the control graph of the given VASS is flat (i.e., without nested cycles). We obtain a family of VASS in dimension 3 whose shortest runs are exponential, and we show that the reachability problem is NP-hard in dimension 7. These results resolve negatively questions that had been posed by the works of Blondin et al. in LICS 2015 and Englert et al. in LICS 2016, and contribute a first construction that distinguishes 3-dimensional flat VASS from 2-dimensional ones. Our third result, by means of a novel family of products of integer fractions, shows that 4-dimensional VASS can have doubly exponentially long shortest runs. The smallest dimension for which this was previously known is 14.
Cite as

Wojciech Czerwiński, Sławomir Lasota, Ranko Lazić, Jérôme Leroux, and Filip Mazowiecki. Reachability in Fixed Dimension Vector Addition Systems with States. In 31st International Conference on Concurrency Theory (CONCUR 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 171, pp. 48:1-48:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{czerwinski_et_al:LIPIcs.CONCUR.2020.48,
  author =	{Czerwi\'{n}ski, Wojciech and Lasota, S{\l}awomir and Lazi\'{c}, Ranko and Leroux, J\'{e}r\^{o}me and Mazowiecki, Filip},
  title =	{{Reachability in Fixed Dimension Vector Addition Systems with States}},
  booktitle =	{31st International Conference on Concurrency Theory (CONCUR 2020)},
  pages =	{48:1--48:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-160-3},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{171},
  editor =	{Konnov, Igor and Kov\'{a}cs, Laura},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2020.48},
  URN =		{urn:nbn:de:0030-drops-128605},
  doi =		{10.4230/LIPIcs.CONCUR.2020.48},
  annote =	{Keywords: reachability problem, vector addition systems, Petri nets}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.FSTTCS.2019.3
Finkel Was Right: Counter-Examples to Several Conjectures on Variants of Vector Addition Systems (Invited Talk)

Authors: Ranko Lazić

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

Abstract
Studying one-dimensional grammar vector addition systems has long been advocated by Alain Finkel. In this presentation, we shall see how research on those systems has led to the recent breakthrough tower lower bound for the reachability problem on vector addition systems, obtained by Czerwiński et al. In fact, we shall look at how appropriate modifications of an underlying technical construction can lead to counter-examples to several conjectures on one-dimensional grammar vector addition systems, fixed-dimensional vector addition systems, and fixed-dimensional flat vector addition systems.
Cite as

Ranko Lazić. Finkel Was Right: Counter-Examples to Several Conjectures on Variants of Vector Addition Systems (Invited Talk). 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. 3:1-3:2, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{lazic:LIPIcs.FSTTCS.2019.3,
  author =	{Lazi\'{c}, Ranko},
  title =	{{Finkel Was Right: Counter-Examples to Several Conjectures on Variants of Vector Addition Systems}},
  booktitle =	{39th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2019)},
  pages =	{3:1--3:2},
  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.2019.3},
  URN =		{urn:nbn:de:0030-drops-115653},
  doi =		{10.4230/LIPIcs.FSTTCS.2019.3},
  annote =	{Keywords: Petri nets, vector addition systems, reachability}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2019.47
Distance Between Mutually Reachable Petri Net Configurations

Authors: Jérôme Leroux

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

Abstract
Petri nets are a classical model of concurrency widely used and studied in formal verification with many applications in modeling and analyzing hardware and software, data bases, and reactive systems. The reachability problem is central since many other problems reduce to reachability questions. In 2011, we proved that a variant of the reachability problem, called the reversible reachability problem is exponential-space complete. Recently, this problem found several unexpected applications in particular in the theory of population protocols. In this paper we revisit the reversible reachability problem in order to prove that the minimal distance in the reachability graph of two mutually reachable configurations is linear with respect to the Euclidean distance between those two configurations.
Cite as

Jérôme Leroux. Distance Between Mutually Reachable Petri Net Configurations. 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. 47:1-47:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{leroux:LIPIcs.FSTTCS.2019.47,
  author =	{Leroux, J\'{e}r\^{o}me},
  title =	{{Distance Between Mutually Reachable Petri Net Configurations}},
  booktitle =	{39th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2019)},
  pages =	{47:1--47:14},
  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.2019.47},
  URN =		{urn:nbn:de:0030-drops-116094},
  doi =		{10.4230/LIPIcs.FSTTCS.2019.47},
  annote =	{Keywords: Petri nets, Vector addition systems, Formal verification, Reachability problem}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.MFCS.2019.5
Petri Net Reachability Problem (Invited Talk)

Authors: Jérôme Leroux

Published in: LIPIcs, Volume 138, 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)

Abstract
Petri nets, also known as vector addition systems, are a long established model of concurrency with extensive applications in modelling and analysis of hardware, software and database systems, as well as chemical, biological and business processes. The central algorithmic problem for Petri nets is reachability: whether from the given initial configuration there exists a sequence of valid execution steps that reaches the given final configuration. The complexity of the problem has remained unsettled since the 1960s, and it is one of the most prominent open questions in the theory of verification. In this presentation, we overview decidability and complexity results over the last fifty years about the Petri net reachability problem.
Cite as

Jérôme Leroux. Petri Net Reachability Problem (Invited Talk). In 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 138, pp. 5:1-5:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{leroux:LIPIcs.MFCS.2019.5,
  author =	{Leroux, J\'{e}r\^{o}me},
  title =	{{Petri Net Reachability Problem}},
  booktitle =	{44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)},
  pages =	{5:1--5:3},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-117-7},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{138},
  editor =	{Rossmanith, Peter and Heggernes, Pinar and Katoen, Joost-Pieter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2019.5},
  URN =		{urn:nbn:de:0030-drops-109493},
  doi =		{10.4230/LIPIcs.MFCS.2019.5},
  annote =	{Keywords: Petri net, Reachability problem, Formal verification, Concurrency}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2018.31
Reachability for Two-Counter Machines with One Test and One Reset

Authors: Alain Finkel, Jérôme Leroux, and Grégoire Sutre

Published in: LIPIcs, Volume 122, 38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2018)

Abstract
We prove that the reachability relation of two-counter machines with one zero-test and one reset is Presburger-definable and effectively computable. Our proof is based on the introduction of two classes of Presburger-definable relations effectively stable by transitive closure. This approach generalizes and simplifies the existing different proofs and it solves an open problem introduced by Finkel and Sutre in 2000.
Cite as

Alain Finkel, Jérôme Leroux, and Grégoire Sutre. Reachability for Two-Counter Machines with One Test and One Reset. In 38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 122, pp. 31:1-31:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{finkel_et_al:LIPIcs.FSTTCS.2018.31,
  author =	{Finkel, Alain and Leroux, J\'{e}r\^{o}me and Sutre, Gr\'{e}goire},
  title =	{{Reachability for Two-Counter Machines with One Test and One Reset}},
  booktitle =	{38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2018)},
  pages =	{31:1--31:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-093-4},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{122},
  editor =	{Ganguly, Sumit and Pandya, Paritosh},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2018.31},
  URN =		{urn:nbn:de:0030-drops-99305},
  doi =		{10.4230/LIPIcs.FSTTCS.2018.31},
  annote =	{Keywords: Counter machine, Vector addition system, Reachability problem, Formal verification, Presburger arithmetic, Infinite-state system}
}
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