International Conference on Foundations of Software Science and Computational Structures

FoSSaCS 2009: Foundations of Software Science and Computational Structures pp 48-62

Logics and Bisimulation Games for Concurrency, Causality and Conflict

  • Julian Gutierrez
Conference paper

DOI: 10.1007/978-3-642-00596-1_5

Volume 5504 of the book series Lecture Notes in Computer Science (LNCS)

Abstract

Based on a simple axiomatization of concurrent behaviour we define two ways of observing parallel computations and show that in each case they are dual to conflict and causality, respectively. We give a logical characterization to those dualities and show that natural fixpoint modal logics can be extracted from such a characterization. We also study the equivalences induced by such logics and prove that they are decidable and can be related with well-known bisimulations for interleaving and noninterleaving concurrency. Moreover, by giving a game-theoretical characterization to the equivalence induced by the main logic, which is called Separation Fixpoint Logic (SFL), we show that the equivalence SFL induces is strictly stronger than a history-preserving bisimulation (hpb) and strictly weaker than a hereditary history-preserving bisimulation (hhpb). Our study considers branching-time models of concurrency based on transition systems and petri net structures.

Keywords

Modal and temporal logicsBisimulation gamesBehavioural equivalencesConcurrent and reactive systemsPetri nets
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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Julian Gutierrez
    • 1
  1. 1.LFCS. School of InformaticsUniversity of Edinburgh, Informatics ForumEdinburghUK