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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Harwood, W., Moller, F., Setzer, A. (2006). Weak Bisimulation Approximants. In: Ésik, Z. (eds) Computer Science Logic. CSL 2006. Lecture Notes in Computer Science, vol 4207. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11874683_24
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DOI: https://doi.org/10.1007/11874683_24
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