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

We introduce the notion of a Real Equation System (RES), which lifts Boolean Equation Systems (BESs) to the domain of extended real numbers. Our RESs allow arbitrary nesting of least and greatest fixed-point operators. We show that each RES can be rewritten into an equivalent RES in normal form. These normal forms provide the basis for a complete procedure to solve RESs. This employs the elimination of the fixed-point variable at the left side of an equation from its right-hand side, combined with a technique often referred to as Gauß-elimination. We illustrate how this framework can be used to verify quantitative modal formulas with alternating fixed-point operators interpreted over probabilistic labelled transition systems.

Jan Friso Groote and Tim A. C. Willemse. Real Equation Systems with Alternating Fixed-Points. In 34th International Conference on Concurrency Theory (CONCUR 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 279, pp. 28:1-28:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{groote_et_al:LIPIcs.CONCUR.2023.28, author = {Groote, Jan Friso and Willemse, Tim A. C.}, title = {{Real Equation Systems with Alternating Fixed-Points}}, booktitle = {34th International Conference on Concurrency Theory (CONCUR 2023)}, pages = {28:1--28:17}, 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.2023.28}, URN = {urn:nbn:de:0030-drops-190225}, doi = {10.4230/LIPIcs.CONCUR.2023.28}, annote = {Keywords: Real Equation System, Solution method, Gau{\ss}-elimination, Model checking, Quantitative modal mu-calculus} }

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

We study the problem of computing minimal distinguishing formulas for non-bisimilar states in finite LTSs. We show that this is NP-hard if the size of the formula must be minimal. Similarly, the existence of a short distinguishing trace is NP-complete. However, we can provide polynomial algorithms, if minimality is formulated as the minimal number of nested modalities, and it can even be extended by recursively requiring a minimal number of nested negations. A prototype implementation shows that the generated formulas are much smaller than those generated by the method introduced by Cleaveland.

Jan Martens and Jan Friso Groote. Computing Minimal Distinguishing Hennessy-Milner Formulas is NP-Hard, but Variants are Tractable. In 34th International Conference on Concurrency Theory (CONCUR 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 279, pp. 32:1-32:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{martens_et_al:LIPIcs.CONCUR.2023.32, author = {Martens, Jan and Groote, Jan Friso}, title = {{Computing Minimal Distinguishing Hennessy-Milner Formulas is NP-Hard, but Variants are Tractable}}, booktitle = {34th International Conference on Concurrency Theory (CONCUR 2023)}, pages = {32:1--32:17}, 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.2023.32}, URN = {urn:nbn:de:0030-drops-190268}, doi = {10.4230/LIPIcs.CONCUR.2023.32}, annote = {Keywords: Distinguishing behaviour, Hennessy-Milner logic, NP-hardness} }

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

An asymptotic lowerbound of Ω((m+n)log n) is established for partition refinement algorithms that decide bisimilarity on labeled transition systems. The lowerbound is obtained by subsequently analysing two families of deterministic transition systems - one with a growing action set and another with a fixed action set.
For deterministic transition systems with a one-letter action set, bisimilarity can be decided with fundamentally different techniques than partition refinement. In particular, Paige, Tarjan, and Bonic give a linear algorithm for this specific situation. We show, exploiting the concept of an oracle, that the approach of Paige, Tarjan, and Bonic is not of help to develop a generic algorithm for deciding bisimilarity on labeled transition systems that is faster than the established lowerbound of Ω((m+n)log n).

Jan Friso Groote, Jan Martens, and Erik de Vink. Bisimulation by Partitioning Is Ω((m+n)log n). In 32nd International Conference on Concurrency Theory (CONCUR 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 203, pp. 31:1-31:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{groote_et_al:LIPIcs.CONCUR.2021.31, author = {Groote, Jan Friso and Martens, Jan and de Vink, Erik}, title = {{Bisimulation by Partitioning Is \Omega((m+n)log n)}}, booktitle = {32nd International Conference on Concurrency Theory (CONCUR 2021)}, pages = {31:1--31:16}, 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.2021.31}, URN = {urn:nbn:de:0030-drops-144087}, doi = {10.4230/LIPIcs.CONCUR.2021.31}, annote = {Keywords: Bisimilarity, partition refinement, labeled transition system, lowerbound} }

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

This article improves the time bound for calculating the weak/branching bisimulation minimisation quotient on state-labelled discrete-time Markov chains from O(m n) to an expected-time O(m log⁴ n), where n is the number of states and m the number of transitions. For these results we assume that the set of state labels AP is small (|AP| ∈ O(m/n log⁴ n)). It follows the ideas of Groote et al. (ACM ToCL 2017) in combination with an efficient algorithm to handle decremental strongly connected components (Bernstein et al., STOC 2019).

David N. Jansen, Jan Friso Groote, Ferry Timmers, and Pengfei Yang. A Near-Linear-Time Algorithm for Weak Bisimilarity on Markov Chains. In 31st International Conference on Concurrency Theory (CONCUR 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 171, pp. 8:1-8:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{jansen_et_al:LIPIcs.CONCUR.2020.8, author = {Jansen, David N. and Groote, Jan Friso and Timmers, Ferry and Yang, Pengfei}, title = {{A Near-Linear-Time Algorithm for Weak Bisimilarity on Markov Chains}}, booktitle = {31st International Conference on Concurrency Theory (CONCUR 2020)}, pages = {8:1--8:20}, 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.2020.8}, URN = {urn:nbn:de:0030-drops-128209}, doi = {10.4230/LIPIcs.CONCUR.2020.8}, annote = {Keywords: Behavioural Equivalence, weak Bisimulation, Markov Chain} }

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**Published in:** Dagstuhl Seminar Proceedings, Volume 6351, Methods for Modelling Software Systems (MMOSS) (2007)

We introduce mCRL2, a specification language that can be used to specify and analyse the behaviour of distributed systems. This language is the successor of the mCRL specification language. The mCRL2 language extends a timed basic process algebra with the possibility to define and use abstract data types. The mCRL2 data language features predefined and higher-order data types. The process algebraic part of mCRL2 allows a faithful translation of coloured Petri nets and component based systems: we have introduced multiactions and we have separated communication and parallelism.

Jan Friso Groote, Aad Mathijssen, Michel Reniers, Yaroslav Usenko, and Muck van Weerdenburg. The Formal Specification Language mCRL2. In Methods for Modelling Software Systems (MMOSS). Dagstuhl Seminar Proceedings, Volume 6351, pp. 1-34, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2007)

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@InProceedings{groote_et_al:DagSemProc.06351.12, author = {Groote, Jan Friso and Mathijssen, Aad and Reniers, Michel and Usenko, Yaroslav and van Weerdenburg, Muck}, title = {{The Formal Specification Language mCRL2}}, booktitle = {Methods for Modelling Software Systems (MMOSS)}, pages = {1--34}, series = {Dagstuhl Seminar Proceedings (DagSemProc)}, ISSN = {1862-4405}, year = {2007}, volume = {6351}, editor = {Ed Brinksma and David Harel and Angelika Mader and Perdita Stevens and Roel Wieringa}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.06351.12}, URN = {urn:nbn:de:0030-drops-8626}, doi = {10.4230/DagSemProc.06351.12}, annote = {Keywords: Specification language, abstract data types, process algebra, operational semantics} }