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**Published in:** LIPIcs, Volume 243, 33rd International Conference on Concurrency Theory (CONCUR 2022)

We consider the class of depth-bounded processes in π-calculus. These processes are the most expressive fragment of π-calculus, for which verification problems are known to be decidable. The decidability of the coverability problem for this class has been achieved by means of well-quasi orders. (Meyer, IFIP TCS 2008; Wies, Zufferey and Henzinger, FoSSaCS 2010). However, the precise complexity of this problem has not been known so far, with only a known EXPSPACE-lower bound.
In this paper, we prove that coverability for depth-bounded processes is 𝐅_ε₀-complete, where 𝐅_ε₀ is a class in the fast-growing hierarchy of complexity classes. This solves an open problem mentioned by Haase, Schmitz, and Schnoebelen (LMCS, Vol 10, Issue 4) and also addresses a question raised by Wies, Zufferey and Henzinger (FoSSaCS 2010).

A. R. Balasubramanian. Complexity of Coverability in Depth-Bounded Processes. In 33rd International Conference on Concurrency Theory (CONCUR 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 243, pp. 17:1-17:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{balasubramanian:LIPIcs.CONCUR.2022.17, author = {Balasubramanian, A. R.}, title = {{Complexity of Coverability in Depth-Bounded Processes}}, booktitle = {33rd International Conference on Concurrency Theory (CONCUR 2022)}, pages = {17:1--17:19}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-246-4}, ISSN = {1868-8969}, year = {2022}, volume = {243}, editor = {Klin, Bartek and Lasota, S{\l}awomir 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.CONCUR.2022.17}, URN = {urn:nbn:de:0030-drops-170809}, doi = {10.4230/LIPIcs.CONCUR.2022.17}, annote = {Keywords: \pi-calculus, Depth-bounded processes, Fast-growing complexity classes} }

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

Broadcast networks are a formalism of distributed computation that allow one to model networks of identical nodes communicating through message broadcasts over a communication topology that does not change over the course of executions. The parameterized verification problem for these networks amounts to proving correctness of a property for any number of nodes, and on all executions. Dually speaking, this problem asks for the existence of an execution of the broadcast network that violates a given property. One specific instance of parameterized verification is the coverability problem which asks whether there is an execution of the network in which some node reaches a given state of the broadcast protocol. This problem was proven to be undecidable by Delzanno, Sangnier and Zavattaro (CONCUR 2010). In the same paper, the authors also prove that, if we additionally assume that the underlying communication topology has a bound on the longest path, then the coverability problem becomes decidable.
In this paper, we provide complexity results for the above problem and prove that the coverability problem for bounded-path topologies is 𝐅_ε₀-complete, where 𝐅_ε₀ is a class in the fast-growing hierarchy of complexity classes. This solves an open problem of Hasse, Schmitz and Schnoebelen (LMCS, Vol 10, Issue 4).

A. R. Balasubramanian. Complexity of Coverability in Bounded Path Broadcast Networks. 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. 35:1-35:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{balasubramanian:LIPIcs.FSTTCS.2021.35, author = {Balasubramanian, A. R.}, title = {{Complexity of Coverability in Bounded Path Broadcast Networks}}, booktitle = {41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021)}, pages = {35:1--35:16}, 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.2021.35}, URN = {urn:nbn:de:0030-drops-155466}, doi = {10.4230/LIPIcs.FSTTCS.2021.35}, annote = {Keywords: Parameterized verification, Bounded path networks, Fast-growing complexity classes} }

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**Published in:** LIPIcs, Volume 203, 32nd International Conference on Concurrency Theory (CONCUR 2021)

We introduce the notion of adaptive synchronisation for pushdown automata, in which there is an external observer who has no knowledge about the current state of the pushdown automaton, but can observe the contents of the stack. The observer would then like to decide if it is possible to bring the automaton from any state into some predetermined state by giving inputs to it in an adaptive manner, i.e., the next input letter to be given can depend on how the contents of the stack changed after the current input letter. We show that for non-deterministic pushdown automata, this problem is 2-EXPTIME-complete and for deterministic pushdown automata, we show EXPTIME-completeness.
To prove the lower bounds, we first introduce (different variants of) subset-synchronisation and show that these problems are polynomial-time equivalent with the adaptive synchronisation problem. We then prove hardness results for the subset-synchronisation problems. For proving the upper bounds, we consider the problem of deciding if a given alternating pushdown system has an accepting run with at most k leaves and we provide an n^O(k²) time algorithm for this problem.

A. R. Balasubramanian and K. S. Thejaswini. Adaptive Synchronisation of Pushdown Automata. In 32nd International Conference on Concurrency Theory (CONCUR 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 203, pp. 17:1-17:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{balasubramanian_et_al:LIPIcs.CONCUR.2021.17, author = {Balasubramanian, A. R. and Thejaswini, K. S.}, title = {{Adaptive Synchronisation of Pushdown Automata}}, booktitle = {32nd International Conference on Concurrency Theory (CONCUR 2021)}, pages = {17:1--17:15}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-203-7}, ISSN = {1868-8969}, year = {2021}, volume = {203}, editor = {Haddad, Serge and Varacca, Daniele}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2021.17}, URN = {urn:nbn:de:0030-drops-143948}, doi = {10.4230/LIPIcs.CONCUR.2021.17}, annote = {Keywords: Adaptive synchronisation, Pushdown automata, Alternating pushdown systems} }

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**Published in:** LIPIcs, Volume 182, 40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2020)

Threshold automata are a formalism for modeling fault-tolerant distributed algorithms. In this paper, we study the parameterized complexity of reachability of threshold automata. As a first result, we show that the problem becomes W[1]-hard even when parameterized by parameters which are quite small in practice. We then consider two restricted cases which arise in practice and provide fixed-parameter tractable algorithms for both these cases. Finally, we report on experimental results conducted on some protocols taken from the literature.

A. R. Balasubramanian. Parameterized Complexity of Safety of Threshold Automata. In 40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 182, pp. 37:1-37:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{balasubramanian:LIPIcs.FSTTCS.2020.37, author = {Balasubramanian, A. R.}, title = {{Parameterized Complexity of Safety of Threshold Automata}}, booktitle = {40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2020)}, pages = {37:1--37:15}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-174-0}, ISSN = {1868-8969}, year = {2020}, volume = {182}, editor = {Saxena, Nitin and Simon, Sunil}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2020.37}, URN = {urn:nbn:de:0030-drops-132787}, doi = {10.4230/LIPIcs.FSTTCS.2020.37}, annote = {Keywords: Threshold automata, distributed algorithms, parameterized complexity} }

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

The Heard-Of model is a simple and relatively expressive model of distributed computation. Because of this, it has gained a considerable attention of the verification community. We give a characterization of all algorithms solving consensus in a fragment of this model. The fragment is big enough to cover many prominent consensus algorithms. The characterization is purely syntactic: it is expressed in terms of some conditions on the text of the algorithm.

A. R. Balasubramanian and Igor Walukiewicz. Characterizing Consensus in the Heard-Of Model. In 31st International Conference on Concurrency Theory (CONCUR 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 171, pp. 9:1-9:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{balasubramanian_et_al:LIPIcs.CONCUR.2020.9, author = {Balasubramanian, A. R. and Walukiewicz, Igor}, title = {{Characterizing Consensus in the Heard-Of Model}}, booktitle = {31st International Conference on Concurrency Theory (CONCUR 2020)}, pages = {9:1--9:18}, 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.2020.9}, URN = {urn:nbn:de:0030-drops-128217}, doi = {10.4230/LIPIcs.CONCUR.2020.9}, annote = {Keywords: consensus problem, Heard-Of model, verification} }