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Divergence and Unique Solution of Equations

Authors Adrien Durier, Daniel Hirschkoff, Davide Sangiorgi

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Adrien Durier
Daniel Hirschkoff
Davide Sangiorgi

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Adrien Durier, Daniel Hirschkoff, and Davide Sangiorgi. Divergence and Unique Solution of Equations. In 28th International Conference on Concurrency Theory (CONCUR 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 85, pp. 11:1-11:16, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2017)


We study proof techniques for bisimilarity based on unique solution of equations. We draw inspiration from a result by Roscoe in the denotational setting of CSP and for failure semantics, essentially stating that an equation (or a system of equations) whose infinite unfolding never produces a divergence has the unique-solution property. We transport this result onto the operational setting of CCS and for bisimilarity. We then exploit the operational approach to: refine the theorem, distinguishing between different forms of divergence; derive an abstract formulation of the theorems, on generic LTSs; adapt the theorems to other equivalences such as trace equivalence, and to preorders such as trace inclusion. We compare the resulting techniques to enhancements of the bisimulation proof method (the ‘up-to techniques’). Finally, we study the theorems in name-passing calculi such as the asynchronous pi-calculus, and revisit the completeness proof of Milner’s encoding of the lambda-calculus into the pi-calculus for Lévy-Longo Trees.
  • Bisimilarity
  • unique solution of equations
  • termination
  • process calculi


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