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DOI: 10.4230/LIPIcs.CONCUR.2019.36

Graded Monads and Graded Logics for the Linear Time - Branching Time Spectrum

Authors: Ulrich Dorsch, Stefan Milius, and Lutz Schröder

Published in: LIPIcs, Volume 140, 30th International Conference on Concurrency Theory (CONCUR 2019)

Abstract

State-based models of concurrent systems are traditionally considered under a variety of notions of process equivalence. In the case of labelled transition systems, these equivalences range from trace equivalence to (strong) bisimilarity, and are organized in what is known as the linear time - branching time spectrum. A combination of universal coalgebra and graded monads provides a generic framework in which the semantics of concurrency can be parametrized both over the branching type of the underlying transition systems and over the granularity of process equivalence. We show in the present paper that this framework of graded semantics does subsume the most important equivalences from the linear time - branching time spectrum. An important feature of graded semantics is that it allows for the principled extraction of characteristic modal logics. We have established invariance of these graded logics under the given graded semantics in earlier work; in the present paper, we extend the logical framework with an explicit propositional layer and provide a generic expressiveness criterion that generalizes the classical Hennessy-Milner theorem to coarser notions of process equivalence. We extract graded logics for a range of graded semantics on labelled transition systems and probabilistic systems, and give exemplary proofs of their expressiveness based on our generic criterion.

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Ulrich Dorsch, Stefan Milius, and Lutz Schröder. Graded Monads and Graded Logics for the Linear Time - Branching Time Spectrum. In 30th International Conference on Concurrency Theory (CONCUR 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 140, pp. 36:1-36:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{dorsch_et_al:LIPIcs.CONCUR.2019.36,
  author =	{Dorsch, Ulrich and Milius, Stefan and Schr\"{o}der, Lutz},
  title =	{{Graded Monads and Graded Logics for the Linear Time - Branching Time Spectrum}},
  booktitle =	{30th International Conference on Concurrency Theory (CONCUR 2019)},
  pages =	{36:1--36:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-121-4},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{140},
  editor =	{Fokkink, Wan and van Glabbeek, Rob},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2019.36},
  URN =		{urn:nbn:de:0030-drops-109384},
  doi =		{10.4230/LIPIcs.CONCUR.2019.36},
  annote =	{Keywords: Linear Time, Branching Time, Monads, System Equivalences, Modal Logics, Expressiveness}
}

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DOI: 10.4230/LIPIcs.CONCUR.2017.32

Efficient Coalgebraic Partition Refinement

Authors: Ulrich Dorsch, Stefan Milius, Lutz Schröder, and Thorsten Wißmann

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

Abstract

We present a generic partition refinement algorithm that quotients coalgebraic systems by behavioural equivalence, an important task in reactive verification; coalgebraic generality implies in particular that we cover not only classical relational systems but also various forms of weighted systems. Under assumptions on the type functor that allow representing its finite coalgebras in terms of nodes and edges, our algorithm runs in time O(m log n) where n and m are the numbers of nodes and edges, respectively. Instances of our generic algorithm thus match the runtime of the best known algorithms for unlabelled transition systems, Markov chains, and deterministic automata (with fixed alphabets), and improve the best known algorithms for Segala systems.

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Ulrich Dorsch, Stefan Milius, Lutz Schröder, and Thorsten Wißmann. Efficient Coalgebraic Partition Refinement. In 28th International Conference on Concurrency Theory (CONCUR 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 85, pp. 32:1-32:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{dorsch_et_al:LIPIcs.CONCUR.2017.32,
  author =	{Dorsch, Ulrich and Milius, Stefan and Schr\"{o}der, Lutz and Wi{\ss}mann, Thorsten},
  title =	{{Efficient Coalgebraic Partition Refinement}},
  booktitle =	{28th International Conference on Concurrency Theory (CONCUR 2017)},
  pages =	{32:1--32:16},
  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.2017.32},
  URN =		{urn:nbn:de:0030-drops-77939},
  doi =		{10.4230/LIPIcs.CONCUR.2017.32},
  annote =	{Keywords: markov chains, deterministic finite automata, partition refinement, generic algorithm, paige-tarjan algorithm, transition systems}
}

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Graded Monads and Graded Logics for the Linear Time - Branching Time Spectrum

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Efficient Coalgebraic Partition Refinement

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