Trustworthy Systems

Divide and congruence III: Stability & divergence


Wan Fokkink, Rob van Glabbeek and Bas Luttik


Vrije Universiteit Amsterdam

Eindhoven University of Technology

UNSW Sydney


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.

BibTeX Entry

    address          = {Berlin, Germany},
    author           = {Fokkink, Wan and van Glabbeek, Robert and Luttik, Bas},
    booktitle        = {International Conference on Concurrency Theory (CONCUR)},
    date             = {2017-9-5},
    doi              = {},
    editor           = {{Meyer, Roland \& Nestmann, Uwe}},
    issn             = {1868-8969},
    keywords         = {Structural Operational Semantics Congruence formats Modal Logic Weak semantics},
    month            = sep,
    pages            = {15:1-15:16},
    paperurl         = {},
    publisher        = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
    series           = {Leibniz International Proceedings in Informatics (LIPIcs)},
    title            = {Divide and Congruence {III}: Stability \& Divergence},
    volume           = {85},
    year             = {2017}