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Divide and Congruence III: Stability & Divergence

Authors Wan Fokkink, Rob van Glabbeek, Bas Luttik



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Wan Fokkink
Rob van Glabbeek
Bas Luttik

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Wan Fokkink, Rob van Glabbeek, and Bas Luttik. Divide and Congruence III: Stability & Divergence. In 28th International Conference on Concurrency Theory (CONCUR 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 85, pp. 15:1-15:16, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2017)
https://doi.org/10.4230/LIPIcs.CONCUR.2017.15

Abstract

In two earlier papers we derived congruence formats for weak semantics on the basis of a decomposition method for modal formulas. The idea is that a congruence format for a semantics must ensure that the formulas in the modal characterisation of this semantics are always decomposed into formulas that are again in this modal characterisation. Here this work is extended with important stability and divergence requirements. Stability refers to the absence of a tau-transition. We show, using the decomposition method, how congruence formats can be relaxed for weak semantics that are stability-respecting. Divergence, which refers to the presence of an infinite sequence of tau-transitions, escapes the inductive decomposition method. We circumvent this problem by proving that a congruence format for a stability-respecting weak semantics is also a congruence format for its divergence-preserving counterpart.
Keywords
  • Structural Operational Semantics
  • Compositionality
  • Congruence
  • Modal Logic
  • Modal Decomposition
  • Weak Semantics
  • Divergence

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