On cool congruence formats for weak bisimulations

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In TCS 146, Bard Bloom presented rule formats for four main notions of bisimulation with silent moves. He proved that weak bisimulation equivalence is a congruence for any process algebra defined by WB cool rules, and established similar results for rooted weak bisimulation (Milner’s “observational congruence”), branching bisimulation and rooted branching bisimulation. This study reformulates Bloom’s results in a more accessible form and contributes analogues for (rooted) η-bisimulation and (rooted) delay bisimulation. Moreover, finite equational axiomatisations of rooted weak bisimulation equivalence are provided that are sound and complete for finite processes in any RWB cool process algebra. These require the introduction of auxiliary operators with lookahead, and an extension of Bloom’s formats for this type of operator with lookahead. Finally, a challenge is presented for which Bloom’s formats fall short and further improvement is called for.
Original languageEnglish
Pages (from-to)3283-3302
Number of pages20
JournalTheoretical Computer Science
Issue number28
Early online date27 Feb 2011
Publication statusPublished - 20 Jun 2011


  • Concurrency
  • Structural operational semantics
  • CCS
  • CSP
  • Branching bisimulation
  • -bisimulation
  • Delay bisimulation
  • Weak bisimulation


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