A Linear Parallel Algorithm to Compute Bisimulation and Relational Coarsest Partitions

Jan Martens; Jan Friso Groote; Lars van den Haak; Pieter Hijma; Anton Wijs

doi:10.1007/978-3-030-90636-8_7

A Linear Parallel Algorithm to Compute Bisimulation and Relational Coarsest Partitions

Jan Martens^*
, Jan Friso Groote
, Lars van den Haak
, Pieter Hijma
, Anton Wijs

^*Corresponding author for this work

Research output: Chapter in Book / Report / Conference proceeding › Conference contribution › Academic › peer-review

Abstract

The most efficient way to calculate strong bisimilarity is by finding the relational coarsest partition of a transition system. We provide the first linear-time algorithm to calculate strong bisimulation using parallel random access machines (PRAMs). More precisely, with n states, m transitions and | Act| ≤ m action labels, we provide an algorithm for max (n, m) processors that calculates strong bisimulation in time O(n+ | Act| ) and space O(n+ m). The best-known PRAM algorithm has time complexity O(nlog n) on a smaller number of processors making it less suitable for massive parallel devices such as GPUs. An implementation on a GPU shows that the linear time-bound is achievable on contemporary hardware.

Original language	English
Title of host publication	Formal Aspects of Component Software
Subtitle of host publication	17th International Conference, FACS 2021, Virtual Event, October 28–29, 2021, Proceedings
Editors	Gwen Salaün, Anton Wijs
Publisher	Springer Science and Business Media Deutschland GmbH
Pages	115-133
Number of pages	19
ISBN (Electronic)	9783030906368
ISBN (Print)	9783030906351
DOIs	https://doi.org/10.1007/978-3-030-90636-8_7
Publication status	Published - 2021
Event	17th International Conference on Formal Aspects of Component Software, FACS 2021 - Virtual, Online Duration: 28 Oct 2021 → 29 Oct 2021

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	13077 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	17th International Conference on Formal Aspects of Component Software, FACS 2021
City	Virtual, Online
Period	28/10/21 → 29/10/21

Bibliographical note

Publisher Copyright:
© 2021, The Author(s).

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

SDG 7 Affordable and Clean Energy

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10.1007/978-3-030-90636-8_7

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Martens, J., Groote, J. F., van den Haak, L., Hijma, P., & Wijs, A. (2021). A Linear Parallel Algorithm to Compute Bisimulation and Relational Coarsest Partitions. In G. Salaün, & A. Wijs (Eds.), Formal Aspects of Component Software: 17th International Conference, FACS 2021, Virtual Event, October 28–29, 2021, Proceedings (pp. 115-133). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 13077 LNCS). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-3-030-90636-8_7

Martens, Jan ; Groote, Jan Friso ; van den Haak, Lars et al. / A Linear Parallel Algorithm to Compute Bisimulation and Relational Coarsest Partitions. Formal Aspects of Component Software: 17th International Conference, FACS 2021, Virtual Event, October 28–29, 2021, Proceedings. editor / Gwen Salaün ; Anton Wijs. Springer Science and Business Media Deutschland GmbH, 2021. pp. 115-133 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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title = "A Linear Parallel Algorithm to Compute Bisimulation and Relational Coarsest Partitions",

abstract = "The most efficient way to calculate strong bisimilarity is by finding the relational coarsest partition of a transition system. We provide the first linear-time algorithm to calculate strong bisimulation using parallel random access machines (PRAMs). More precisely, with n states, m transitions and | Act| ≤ m action labels, we provide an algorithm for max (n, m) processors that calculates strong bisimulation in time O(n+ | Act| ) and space O(n+ m). The best-known PRAM algorithm has time complexity O(nlog n) on a smaller number of processors making it less suitable for massive parallel devices such as GPUs. An implementation on a GPU shows that the linear time-bound is achievable on contemporary hardware.",

author = "Jan Martens and Groote, \{Jan Friso\} and \{van den Haak\}, Lars and Pieter Hijma and Anton Wijs",

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doi = "10.1007/978-3-030-90636-8\_7",

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Martens, J, Groote, JF, van den Haak, L, Hijma, P & Wijs, A 2021, A Linear Parallel Algorithm to Compute Bisimulation and Relational Coarsest Partitions. in G Salaün & A Wijs (eds), Formal Aspects of Component Software: 17th International Conference, FACS 2021, Virtual Event, October 28–29, 2021, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 13077 LNCS, Springer Science and Business Media Deutschland GmbH, pp. 115-133, 17th International Conference on Formal Aspects of Component Software, FACS 2021, Virtual, Online, 28/10/21. https://doi.org/10.1007/978-3-030-90636-8_7

A Linear Parallel Algorithm to Compute Bisimulation and Relational Coarsest Partitions. / Martens, Jan; Groote, Jan Friso; van den Haak, Lars et al.
Formal Aspects of Component Software: 17th International Conference, FACS 2021, Virtual Event, October 28–29, 2021, Proceedings. ed. / Gwen Salaün; Anton Wijs. Springer Science and Business Media Deutschland GmbH, 2021. p. 115-133 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 13077 LNCS).

Research output: Chapter in Book / Report / Conference proceeding › Conference contribution › Academic › peer-review

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AU - Wijs, Anton

PY - 2021

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N2 - The most efficient way to calculate strong bisimilarity is by finding the relational coarsest partition of a transition system. We provide the first linear-time algorithm to calculate strong bisimulation using parallel random access machines (PRAMs). More precisely, with n states, m transitions and | Act| ≤ m action labels, we provide an algorithm for max (n, m) processors that calculates strong bisimulation in time O(n+ | Act| ) and space O(n+ m). The best-known PRAM algorithm has time complexity O(nlog n) on a smaller number of processors making it less suitable for massive parallel devices such as GPUs. An implementation on a GPU shows that the linear time-bound is achievable on contemporary hardware.

AB - The most efficient way to calculate strong bisimilarity is by finding the relational coarsest partition of a transition system. We provide the first linear-time algorithm to calculate strong bisimulation using parallel random access machines (PRAMs). More precisely, with n states, m transitions and | Act| ≤ m action labels, we provide an algorithm for max (n, m) processors that calculates strong bisimulation in time O(n+ | Act| ) and space O(n+ m). The best-known PRAM algorithm has time complexity O(nlog n) on a smaller number of processors making it less suitable for massive parallel devices such as GPUs. An implementation on a GPU shows that the linear time-bound is achievable on contemporary hardware.

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Martens J, Groote JF, van den Haak L, Hijma P, Wijs A. A Linear Parallel Algorithm to Compute Bisimulation and Relational Coarsest Partitions. In Salaün G, Wijs A, editors, Formal Aspects of Component Software: 17th International Conference, FACS 2021, Virtual Event, October 28–29, 2021, Proceedings. Springer Science and Business Media Deutschland GmbH. 2021. p. 115-133. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). Epub 2021 Oct 28. doi: 10.1007/978-3-030-90636-8_7

A Linear Parallel Algorithm to Compute Bisimulation and Relational Coarsest Partitions

Abstract

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Bibliographical note

UN SDGs

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