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

**Published in:** LIPIcs, Volume 229, 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)

We consider the distributed control synthesis problem for systems with locks. The goal is to find local controllers so that the global system does not deadlock. With no restriction this problem is undecidable even for three processes each using a fixed number of locks. We propose two restrictions that make distributed control decidable. The first one is to allow each process to use at most two locks. The problem then becomes complete for the second level of the polynomial time hierarchy, and even in Ptime under some additional assumptions. The dining philosophers problem satisfies these assumptions. The second restriction is a nested usage of locks. In this case the synthesis problem is Nexptime-complete. The drinking philosophers problem falls in this case.

Hugo Gimbert, Corto Mascle, Anca Muscholl, and Igor Walukiewicz. Distributed Controller Synthesis for Deadlock Avoidance. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 125:1-125:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{gimbert_et_al:LIPIcs.ICALP.2022.125, author = {Gimbert, Hugo and Mascle, Corto and Muscholl, Anca and Walukiewicz, Igor}, title = {{Distributed Controller Synthesis for Deadlock Avoidance}}, booktitle = {49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)}, pages = {125:1--125:20}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-235-8}, ISSN = {1868-8969}, year = {2022}, volume = {229}, editor = {Boja\'{n}czyk, Miko{\l}aj and Merelli, Emanuela and Woodruff, David P.}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2022.125}, URN = {urn:nbn:de:0030-drops-164668}, doi = {10.4230/LIPIcs.ICALP.2022.125}, annote = {Keywords: Distributed Synthesis, Concurrency, Lock Synchronisation, Deadlock Avoidance} }

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**Published in:** LIPIcs, Volume 118, 29th International Conference on Concurrency Theory (CONCUR 2018)

We introduce a new class of automata on infinite trees called alternating nonzero automata, which extends the class of non-deterministic nonzero automata. The emptiness problem for this class is still open, however we identify a subclass, namely limited choice, for which we reduce the emptiness problem for alternating nonzero automata to the same problem for non-deterministic ones, which implies decidability. We obtain, as corollaries, algorithms for the satisfiability of a probabilistic temporal logic extending both CTL* and the qualitative fragment of pCTL*.

Paulin Fournier and Hugo Gimbert. Alternating Nonzero Automata. In 29th International Conference on Concurrency Theory (CONCUR 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 118, pp. 13:1-13:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{fournier_et_al:LIPIcs.CONCUR.2018.13, author = {Fournier, Paulin and Gimbert, Hugo}, title = {{Alternating Nonzero Automata}}, booktitle = {29th International Conference on Concurrency Theory (CONCUR 2018)}, pages = {13:1--13:16}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-087-3}, ISSN = {1868-8969}, year = {2018}, volume = {118}, editor = {Schewe, Sven and Zhang, Lijun}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2018.13}, URN = {urn:nbn:de:0030-drops-95517}, doi = {10.4230/LIPIcs.CONCUR.2018.13}, annote = {Keywords: zero-automata, probabilities, temporal logics} }

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**Published in:** LIPIcs, Volume 93, 37th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2017)

The decidability of the distributed version of the Ramadge and Wonham controller synthesis problem,
where both the plant and the controllers are modeled as asynchronous automata
and the controllers have causal memory
is a challenging open problem.
There exist three classes of plants for which the existence of a correct controller with causal memory has been shown decidable: when the dependency graph of actions is series-parallel,
when the processes are connectedly communicating and when the dependency graph of processes is a tree.
We design a class of plants, called decomposable games,
with a decidable controller synthesis problem.
This provides
a unified proof of the three existing decidability results
as well as new examples of decidable plants.

Hugo Gimbert. On the Control of Asynchronous Automata. In 37th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 93, pp. 30:1-30:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{gimbert:LIPIcs.FSTTCS.2017.30, author = {Gimbert, Hugo}, title = {{On the Control of Asynchronous Automata}}, booktitle = {37th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2017)}, pages = {30:1--30:15}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-055-2}, ISSN = {1868-8969}, year = {2018}, volume = {93}, editor = {Lokam, Satya and Ramanujam, R.}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2017.30}, URN = {urn:nbn:de:0030-drops-84142}, doi = {10.4230/LIPIcs.FSTTCS.2017.30}, annote = {Keywords: Asynchronous automata, Controller synthesis} }

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**Published in:** LIPIcs, Volume 85, 28th International Conference on Concurrency Theory (CONCUR 2017)

We introduce a new setting where a population of agents, each modelled by a finite-state system, are controlled uniformly: the controller applies the same action to every agent. The framework is largely inspired by the control of a biological system, namely a population of yeasts, where the controller may only change the environment common to all cells. We study a synchronisation problem for such populations: no matter how individual agents react to the actions of the controller, the controller aims at driving all agents synchronously to a target state. The agents are naturally represented by a non-deterministic finite state automaton (NFA), the same for every agent, and the whole system is encoded as a 2-player game. The first player chooses actions, and the second player resolves non-determinism for each agent. The game with m agents is called the m-population game. This gives rise to a parameterized control problem (where control refers to 2 player games), namely the population control problem: can playerone control the m-population game for all m in N whatever playertwo does?
In this paper, we prove that the population control problem is decidable, and it is a EXPTIME-complete problem. As far as we know, this is one of the first results on parameterized control. Our algorithm, not based on cut-off techniques, produces winning strategies which are symbolic, that i they do not need to count precisely how the population is spread between states. We also show that if the is no winning strategy, then there is a population size cutoff such that playerone wins the m-population game if and only if m< \cutoff. Surprisingly, \cutoff can be doubly exponential in the number of states of the NFA, with tight upper and lower bounds.

Nathalie Bertrand, Miheer Dewaskar, Blaise Genest, and Hugo Gimbert. Controlling a Population. In 28th International Conference on Concurrency Theory (CONCUR 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 85, pp. 12:1-12:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{bertrand_et_al:LIPIcs.CONCUR.2017.12, author = {Bertrand, Nathalie and Dewaskar, Miheer and Genest, Blaise and Gimbert, Hugo}, title = {{Controlling a Population}}, booktitle = {28th International Conference on Concurrency Theory (CONCUR 2017)}, pages = {12:1--12:16}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-048-4}, ISSN = {1868-8969}, year = {2017}, volume = {85}, editor = {Meyer, Roland and Nestmann, Uwe}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2017.12}, URN = {urn:nbn:de:0030-drops-78000}, doi = {10.4230/LIPIcs.CONCUR.2017.12}, annote = {Keywords: Model-checking, control, parametric systems} }

Document

**Published in:** LIPIcs, Volume 80, 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)

Zero automata are a probabilistic extension of parity automata on infinite trees. The satisfiability of a certain probabilistic variant of MSO, called TMSO+zero, reduces to the emptiness problem for zero automata. We introduce a variant of zero automata called nonzero automata. We prove that for every zero automaton there is an equivalent nonzero automaton of quadratic size
and the emptiness problem of nonzero automata is decidable, with complexity co-NP. These results imply that TMSO+zero has decidable satisfiability.

Mikolaj Bojanczyk, Hugo Gimbert, and Edon Kelmendi. Emptiness of Zero Automata Is Decidable. In 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 80, pp. 106:1-106:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{bojanczyk_et_al:LIPIcs.ICALP.2017.106, author = {Bojanczyk, Mikolaj and Gimbert, Hugo and Kelmendi, Edon}, title = {{Emptiness of Zero Automata Is Decidable}}, booktitle = {44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)}, pages = {106:1--106:13}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-041-5}, ISSN = {1868-8969}, year = {2017}, volume = {80}, editor = {Chatzigiannakis, Ioannis and Indyk, Piotr and Kuhn, Fabian and Muscholl, Anca}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2017.106}, URN = {urn:nbn:de:0030-drops-74745}, doi = {10.4230/LIPIcs.ICALP.2017.106}, annote = {Keywords: tree automata, probabilistic automata, monadic second-order logic} }

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