Weak Bisimulation Approximants

  • Will Harwood
  • Faron Moller
  • Anton Setzer
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4207)

Abstract

Bisimilarity and weak bisimilarity ≈ are canonical notions of equivalence between processes, which are defined co-inductively, but may be approached – and even reached – by their (transfinite) inductively-defined approximants ~ α and ≈ α . For arbitrary processes this approximation may need to climb arbitrarily high through the infinite ordinals before stabilising. In this paper we consider a simple yet well-studied process algebra, the Basic Parallel Processes (BPP), and investigate for this class of processes the minimal ordinal α such that ≈ = ≈ α .

The main tool in our investigation is a novel proof of Dickson’s Lemma. Unlike classical proofs, the proof we provide gives rise to a tight ordinal bound, of ω n , on the order type of non-increasing sequences of n-tuples of natural numbers. With this we are able to reduce a long-standing bound on the approximation hierarchy for weak bisimilarity ≈ over BPP, and show that \({\approx} = {\approx_{\omega^\omega}}\).

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Will Harwood
    • 1
  • Faron Moller
    • 1
  • Anton Setzer
    • 1
  1. 1.Department of Computer ScienceSwansea UniversitySketty, SwanseaUK

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