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Divide and Congruence III: Stability & Divergence Fokkink, Wan van Glabbeek, Rob Luttik, Bas Structural Operational Semantics Compositionality Congruence Modal Logic Modal Decomposition Weak Semantics Divergence 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Wan Fokkink and Rob van Glabbeek and Bas Luttik 2017 Is Part Of LIPIcs, Volume 85, 28th International Conference on Concurrency Theory (CONCUR 2017) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.CONCUR.2017.15 urn:nbn:de:0030-drops-77855 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2017.15 eng https://creativecommons.org/licenses/by/3.0/legalcode