research-article

A Logic for True Concurrency

Authors:

Silvia CrafaAuthors Info & Claims

Journal of the ACM (JACM), Volume 61, Issue 4

Article No.: 24, Pages 1 - 36

https://doi.org/10.1145/2629638

Published: 01 July 2014 Publication History

Abstract

We propose a logic for true concurrency whose formulae predicate about events in computations and their causal dependencies. The induced logical equivalence is hereditary history-preserving bisimilarity, and fragments of the logic can be identified which correspond to other true concurrent behavioural equivalences in the literature: step, pomset and history-preserving bisimilarity. Standard Hennessy-Milner logic, and thus (interleaving) bisimilarity, is also recovered as a fragment. We also propose an extension of the logic with fixpoint operators, thus allowing to describe causal and concurrency properties of infinite computations. This work contributes to a rational presentation of the true concurrent spectrum and to a deeper understanding of the relations between the involved behavioural equivalences.

References

[1]

Paolo Baldan and Silvia Crafa. 2010. A logic for true concurrency. In Proceedings of CONCUR’10, Paul Gastin and François Laroussinie, Eds., Lecture Notes in Computer Science, vol. 6269, Springer, Berlin, 147--161.

Digital Library

[2]

Marek A. Bednarczyk. 1991. Hereditary history preserving bisimulations or what is the power of the future perfect in program logics. Tech. Rep. Polish Academy of Sciences.

[3]

Eike Best, Raymond Devillers, Astrid Kiehn, and Lucia Pomello. 1991. Fully concurrent bisimulation. Acta Inf. 28, 231--261.

Digital Library

[4]

Julian Bradfield and Sibylle B. Fröschle. 2002. Independence-friendly modal logic and True Concurrency. Nord. J. Comput. 9, 1 (2002), 102--117.

Digital Library

[5]

Julian Bradfield and Stephan Kreutzer. 2005. The complexity of independence-friendly fixpoint logic. In Proceedings of CLS’05, C.-H. Luke Ong, Ed., Lecture Notes in Computer Science, vol. 3634, Springer, Berlin, 355--368.

Digital Library

[6]

Julian Bradfield and Colin Stirling. 2006. Modal mu-calculi. In Handbook of Modal Logic, Patrick Blackburn, Johan van Benthem, and Franck Wolter, Eds., Elsevier, Amsterdam, The Netherlands, 721--756.

[7]

Ferroudja Cherief. 1992. Back and forth bisimulations on prime event structures. In Proceedings of PARLE’92, Daniel Etiemble and Jean-Claude Syre, Eds., Lecture Notes in Computer Science, vol. 605, Springer, Berlin, 843--858.

Digital Library

[8]

Mads Dam. 1996. Model checking mobile processes. Inf. Computat. 129, 1, 35--51.

Digital Library

[9]

Mads Dam, Lars-Åke Fredlund, and Dilian Gurov. 1998. Toward parametric verification of open distributed systems. In Proceedings of COMPOS’97, Willem P. de Roever, Hans Langmaack, and Amir Pnueli, Eds., Lecture Notes in Computer Science, vol. 1536, Springer, Berlin, 150--185.

Digital Library

[10]

Rocco De Nicola and Gianluigi Ferrari. 1990. Observational logics and concurrency models. In Proceedings of FST-TCS’90, Kesav V. Nori and C. E. Veni Madhavan, Eds., Lecture Notes in Computer Science, vol. 472, Springer, Berlin, 301--315.

Digital Library

[11]

Pierpaolo Degano, Rocco De Nicola, and Ugo Montanari. 1988. Partial orderings descriptions and observations of nondeterministic concurrent processes. In REX Workshop, Jaco W. de Bakker, Willem P. de Roever, and Grzegorz Rozenberg, Eds., Lecture Notes in Computer Science, vol. 354, Springer, Berlin, 438--466.

Digital Library

[12]

Sibylle B. Fröschle and Thomas T. Hildebrandt. 1999. On plain and hereditary history-preserving bisimulation. In Proceedings of MFCS’99, Miroslaw Kutylowski, Leszek Pacholski, and Tomasz Wierzbicki, Eds., Lecture Notes in Computer Science, vol. 1672, Springer, Berlin, 354--365.

Digital Library

[13]

Jan Friso Groote and Tim A. C. Willemse. 2005. Model-checking processes with data. Sci. Comput. Prog. 56, 3, 251--273.

Digital Library

[14]

Julian Gutierrez. 2009. Logics and bisimulation games for concurrency, causality and conflict. In Proceedings of FoSSaCS’09, Luca de Alfaro, Ed., Lecture Notes in Computer Science, vol. 5504, Springer, Berlin, 48--62.

Digital Library

[15]

Julian Gutierrez. 2011. On bisimulation and model-checking for concurrent systems with partial order semantics. Ph.D. dissertation. LFCS - University of Edinburgh.

[16]

Julian Gutierrez and Julian C. Bradfield. 2009. Model-checking games for fixpoint logics with partial order models. In Proceedings of CONCUR’09, Mario Bravetti and Gianluigi Zavattaro, Eds., Lecture Notes in Computer Science, vol. 5710, Springer, Berlin, 354--368.

Digital Library

[17]

Matthew Hennessy and Robin Milner. 1985. Algebraic laws for nondeterminism and concurrency. J. ACM 32, 137--161.

Digital Library

[18]

Matthew Hennessy and Colin Stirling. 1985. The power of the future perfect in program logics. Inf. Cont. 67, 1--3, 23--52.

Digital Library

[19]

André Joyal, Mogens Nielsen, and Glynn Winskel. 1996. Bisimulation from open maps. Inf. Computat. 127, 2, 164--185. (Originally BRICS Report Series RS-94-7.)

Digital Library

[20]

Marcin Jurdzinski, Mogens Nielsen, and Jirí Srba. 2003. Undecidability of domino games and HHP-bisimilarity. Inf. Computat. 184, 2, 343--368.

Digital Library

[21]

Ugo Montanari and Marco Pistore. 1997. Minimal transition systems for history-preserving bisimulation. In Proceedings of STACS’97, Rüdiger Reischuk and Michel Morvan, Eds., Lecture Notes in Computer Science, vol. 1200, Springer, Berlin, 413--425.

Digital Library

[22]

Mogens Nielsen and Christian Clausen. 1995. Games and logics for a noninterleaving bisimulation. Nord. J. Comput. 2, 2, 221--249.

Digital Library

[23]

Mogens Nielsen, Gordon D. Plotkin, and Glynn Winskel. 1981. Petri nets, event structures and domains, Part I. Theoret. Comput. Sci. 13, 85--108.

[24]

Wojciech Penczek. 1995. Branching time and partial order in temporal logics. In Time and Logic: A Computational Approach, Leonard Bolc and Andrzej Szałas, Eds., UCL Press, London, UK, 179--228.

Digital Library

[25]

Iain Phillips and Irek Ulidowski. 2010. Reverse bisimulations on stable configuration structures. In Proceedings of SOS’09, B. Klin and P. Sobociǹski, Eds., Electronic Proceedings in Theoretical Computer Science, vol. 18. Elsevier, Amsterdam, The Netherlands, 62--76.

[26]

Iain Phillips and Irek Ulidowski. 2011. A logic with reverse modalities for history-preserving bisimulations. In Proceedings of EXPRESS’11, Bas Luttik and Frank Valencia, Eds., Electronic Proceedings in Theoretical Computer Science, vol. 64, Elsevier, Amsterdam, The Netherlands, 104--118.

[27]

Sophie Pinchinat, François Laroussinie, and Philippe Schnoebelen. 1994. Logical characterization of truly concurrent bisimulation. Tech. Rep. 114. LIFIA-IMAG, Grenoble.

[28]

Alexander M. Rabinovich and Boris A. Trakhtenbrot. 1988. Behaviour structures and nets. Fund. Inf. 11, 357--404.

[29]

Rob J. van Glabbeek. 2001. The linear time -- branching time spectrum I: The semantics of concrete, sequential processes. In Handbook of Process Algebra, Jan A. Bergstra, Alban Ponse, and Scott A. Smolka, Eds., Elsevier, Amsterdam, The Netherlands, 3--99.

[30]

Rob J. van Glabbeek and Ursula Goltz. 2001. Refinement of actions and equivalence notions for concurrent systems. Acta Inf. 37, 4/5, 229--327.

Digital Library

[31]

Walter Vogler. 1991. Deciding history preserving bisimilarity. In Proceedings of ICALP’91, Javier Leach Albert, Burkhard Monien, and Mario Rodríguez-Artalejo, Eds., Lecture Notes in Computer Science, vol. 510, Springer, Berlin, 495--505.

Digital Library

[32]

Glynn Winskel. 1987. Event structures. In Petri Nets: Applications and Relationships to Other Models of Concurrency, Wilfried Brauer, Wolfgang Reisig, and Grzegorz Rozenberg, Eds., Lecture Notes in Computer Science, vol. 255, Springer, Berlin, 325--392.

Digital Library

[33]

Glynn Winskel and Mogens Nielsen. 1995. Models for concurrency. In Samson Abramsky, Dov M. Gabbay, and Thomas S. E. Maibaum, Eds., Handbook of logic in Computer Science, vol. 4, Clarendon Press, Oxford, UK.

Digital Library

Cited By

Polyvyanyy Ater Hofstede ALa Rosa MOuyang CPika A(2024)Process Query Language: Design, Implementation, and EvaluationInformation Systems10.1016/j.is.2023.102337122(102337)Online publication date: May-2024
https://doi.org/10.1016/j.is.2023.102337
Horne RMauw SYurkov S(2023)When privacy fails, a formula describes an attackTheoretical Computer Science10.1016/j.tcs.2023.113842959:COnline publication date: 30-May-2023
https://dl.acm.org/doi/10.1016/j.tcs.2023.113842
(2023)ReferencesAlgebraic Theory for True Concurrency10.1016/B978-0-44-318912-8.00013-9(213-214)Online publication date: 2023
https://doi.org/10.1016/B978-0-44-318912-8.00013-9
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Index Terms

A Logic for True Concurrency
1. Computing methodologies
  1. Artificial intelligence
    1. Knowledge representation and reasoning
      1. Temporal reasoning
2. Theory of computation

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Published In

cover image Journal of the ACM

Journal of the ACM Volume 61, Issue 4

July 2014

259 pages

ISSN:0004-5411

EISSN:1557-735X

DOI:10.1145/2660259

Editor:
Victor Vianu
University of California, San Diego

Issue’s Table of Contents

Copyright © 2014 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than the author(s) must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected].

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Publication History

Published: 01 July 2014

Accepted: 01 April 2014

Revised: 01 December 2013

Received: 01 October 2011

Published in JACM Volume 61, Issue 4

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Cited By

Polyvyanyy Ater Hofstede ALa Rosa MOuyang CPika A(2024)Process Query Language: Design, Implementation, and EvaluationInformation Systems10.1016/j.is.2023.102337122(102337)Online publication date: May-2024
https://doi.org/10.1016/j.is.2023.102337
Horne RMauw SYurkov S(2023)When privacy fails, a formula describes an attackTheoretical Computer Science10.1016/j.tcs.2023.113842959:COnline publication date: 30-May-2023
https://dl.acm.org/doi/10.1016/j.tcs.2023.113842
(2023)ReferencesAlgebraic Theory for True Concurrency10.1016/B978-0-44-318912-8.00013-9(213-214)Online publication date: 2023
https://doi.org/10.1016/B978-0-44-318912-8.00013-9
Wang Y(2023)Algebraic laws for true concurrencyAlgebraic Theory for True Concurrency10.1016/B978-0-44-318912-8.00009-7(49-158)Online publication date: 2023
https://doi.org/10.1016/B978-0-44-318912-8.00009-7
Wang Y(2023)IntroductionAlgebraic Theory for True Concurrency10.1016/B978-0-44-318912-8.00006-1(1-5)Online publication date: 2023
https://doi.org/10.1016/B978-0-44-318912-8.00006-1
Baldan PGorla DPadoan TSalvo I(2022)Behavioural logics for configuration structuresTheoretical Computer Science10.1016/j.tcs.2022.02.018913(94-112)Online publication date: Apr-2022
https://doi.org/10.1016/j.tcs.2022.02.018
Baldan PGorla DPadoan TSalvo I(2022)Characterising spectra of equivalences for event structures, logicallyInformation and Computation10.1016/j.ic.2022.104887285(104887)Online publication date: May-2022
https://doi.org/10.1016/j.ic.2022.104887
Gorrieri R(2021)A Study on Team Bisimulation and H-team Bisimulation for BPP NetsTheoretical Computer Science10.1016/j.tcs.2021.09.037Online publication date: Sep-2021
https://doi.org/10.1016/j.tcs.2021.09.037
Gorrieri R(2021)Team bisimilarity, and its associated modal logic, for BPP netsActa Informatica10.1007/s00236-020-00377-458:5(529-569)Online publication date: 1-Oct-2021
https://dl.acm.org/doi/10.1007/s00236-020-00377-4
Baldan PPadoan T(2020)Model Checking a Logic for True ConcurrencyACM Transactions on Computational Logic10.1145/341285321:4(1-49)Online publication date: 26-Oct-2020
https://dl.acm.org/doi/10.1145/3412853
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