Search Results

Documents authored by Sznajder, Nathalie

Document
DOI: 10.4230/LIPIcs.MFCS.2026.57
Model Checking with Temporal Graphs and Their Derivative

Authors: Binh-Minh Bui-Xuan, Florent Krasnopol, Bruno Monasson, and Nathalie Sznajder

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

Abstract
Temporal graphs are graphs where the presence or properties of their vertices and edges change over time. When time is discrete, a temporal graph can be defined as a sequence of static graphs over a discrete time span, called lifetime, or as a single graph where each edge is associated with a specific set of time instants where the edge is alive. For static graphs, Courcelle’s Theorem asserts that any graph problem expressible in monadic second-order logic can be solved in linear time on graphs of bounded tree-width. We propose the first adaptation of Courcelle’s Theorem for monadic second-order logic on temporal graphs that does not explicitly rely on a parameter proportional to the lifetime, or defined as the maximum number of time-edges incident with any vertex which in the worst case is higher than the lifetime. We then introduce the notion of derivative over a sliding time window of a chosen size, and define the tree-width and twin-width of the temporal graph’s derivative. We exemplify its usefulness with meta-theorems with respect to a temporal variant of first-order logic. The resulting logic expresses a wide range of temporal graph problems including a version of temporal cliques, an important notion when querying time series databases for community structures.
Cite as

Binh-Minh Bui-Xuan, Florent Krasnopol, Bruno Monasson, and Nathalie Sznajder. Model Checking with Temporal Graphs and Their Derivative. In 51st International Symposium on Mathematical Foundations of Computer Science (MFCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 386, pp. 57:1-57:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

Copy BibTex To Clipboard

@InProceedings{buixuan_et_al:LIPIcs.MFCS.2026.57,
  author =	{Bui-Xuan, Binh-Minh and Krasnopol, Florent and Monasson, Bruno and Sznajder, Nathalie},
  title =	{{Model Checking with Temporal Graphs and Their Derivative}},
  booktitle =	{51st International Symposium on Mathematical Foundations of Computer Science (MFCS 2026)},
  pages =	{57:1--57:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-442-0},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{386},
  editor =	{Kouck\'{y}, Michal and Petrișan, Daniela},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2026.57},
  URN =		{urn:nbn:de:0030-drops-274393},
  doi =		{10.4230/LIPIcs.MFCS.2026.57},
  annote =	{Keywords: temporal graphs, dynamic network, tree decomposition, monadic second order logic, first order logic, derivative}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2025.53
Wait-Only Broadcast Protocols Are Easier to Verify

Authors: Lucie Guillou, Arnaud Sangnier, and Nathalie Sznajder

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

Abstract
We study networks of processes that all execute the same finite-state protocol and communicate via broadcasts. We are interested in two problems with a parameterized number of processes: the synchronization problem which asks whether there is an execution which puts all processes on a given state; and the repeated coverability problem which asks if there is an infinite execution where a given transition is taken infinitely often. Since both problems are undecidable in the general case, we investigate those problems when the protocol is Wait-Only, i.e., it has no state from which a process can both broadcast and receive messages. We establish that the synchronization problem becomes Ackermann-complete, and the repeated coverability problem is in ExpSpace and PSpace-hard.
Cite as

Lucie Guillou, Arnaud Sangnier, and Nathalie Sznajder. Wait-Only Broadcast Protocols Are Easier to Verify. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 53:1-53:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{guillou_et_al:LIPIcs.MFCS.2025.53,
  author =	{Guillou, Lucie and Sangnier, Arnaud and Sznajder, Nathalie},
  title =	{{Wait-Only Broadcast Protocols Are Easier to Verify}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{53:1--53:17},
  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.2025.53},
  URN =		{urn:nbn:de:0030-drops-241609},
  doi =		{10.4230/LIPIcs.MFCS.2025.53},
  annote =	{Keywords: Parameterised verification, Reachability, Broadcast}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2024.26
Phase-Bounded Broadcast Networks over Topologies of Communication

Authors: Lucie Guillou, Arnaud Sangnier, and Nathalie Sznajder

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

Abstract
We study networks of processes that all execute the same finite state protocol and that communicate through broadcasts. The processes are organized in a graph (a topology) and only the neighbors of a process in this graph can receive its broadcasts. The coverability problem asks, given a protocol and a state of the protocol, whether there is a topology for the processes such that one of them (at least) reaches the given state. This problem is undecidable [G. Delzanno et al., 2010]. We study here an under-approximation of the problem where processes alternate a bounded number of times k between phases of broadcasting and phases of receiving messages. We show that, if the problem remains undecidable when k is greater than 6, it becomes decidable for k = 2, and ExpSpace-complete for k = 1. Furthermore, we show that if we restrict ourselves to line topologies, the problem is in P for k = 1 and k = 2.
Cite as

Lucie Guillou, Arnaud Sangnier, and Nathalie Sznajder. Phase-Bounded Broadcast Networks over Topologies of Communication. In 35th International Conference on Concurrency Theory (CONCUR 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 311, pp. 26:1-26:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{guillou_et_al:LIPIcs.CONCUR.2024.26,
  author =	{Guillou, Lucie and Sangnier, Arnaud and Sznajder, Nathalie},
  title =	{{Phase-Bounded Broadcast Networks over Topologies of Communication}},
  booktitle =	{35th International Conference on Concurrency Theory (CONCUR 2024)},
  pages =	{26:1--26:16},
  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.2024.26},
  URN =		{urn:nbn:de:0030-drops-207987},
  doi =		{10.4230/LIPIcs.CONCUR.2024.26},
  annote =	{Keywords: Parameterized verification, Coverability, Broadcast Networks}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2023.7
Safety Analysis of Parameterised Networks with Non-Blocking Rendez-Vous

Authors: Lucie Guillou, Arnaud Sangnier, and Nathalie Sznajder

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

Abstract
We consider networks of processes that all execute the same finite-state protocol and communicate via a rendez-vous mechanism. When a process requests a rendez-vous, another process can respond to it and they both change their control states accordingly. We focus here on a specific semantics, called non-blocking, where the process requesting a rendez-vous can change its state even if no process can respond to it. In this context, we study the parameterised coverability problem of a configuration, which consists in determining whether there is an initial number of processes and an execution allowing to reach a configuration bigger than a given one. We show that this problem is EXPSPACE-complete and can be solved in polynomial time if the protocol is partitioned into two sets of states, the states from which a process can request a rendez-vous and the ones from which it can answer one. We also prove that the problem of the existence of an execution bringing all the processes in a final state is undecidable in our context. These two problems can be solved in polynomial time with the classical rendez-vous semantics.
Cite as

Lucie Guillou, Arnaud Sangnier, and Nathalie Sznajder. Safety Analysis of Parameterised Networks with Non-Blocking Rendez-Vous. In 34th International Conference on Concurrency Theory (CONCUR 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 279, pp. 7:1-7:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

Copy BibTex To Clipboard

@InProceedings{guillou_et_al:LIPIcs.CONCUR.2023.7,
  author =	{Guillou, Lucie and Sangnier, Arnaud and Sznajder, Nathalie},
  title =	{{Safety Analysis of Parameterised Networks with Non-Blocking Rendez-Vous}},
  booktitle =	{34th International Conference on Concurrency Theory (CONCUR 2023)},
  pages =	{7:1--7:17},
  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.2023.7},
  URN =		{urn:nbn:de:0030-drops-190015},
  doi =		{10.4230/LIPIcs.CONCUR.2023.7},
  annote =	{Keywords: Parameterised verification, Coverability, Counter machines}
}
Any Issues?
X

Feedback on the Current Page

CAPTCHA

Thanks for your feedback!

Feedback submitted to Dagstuhl Publishing

Could not send message

Please try again later or send an E-mail
© 2023-2026 Schloss Dagstuhl – LZI GmbH Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact