Trustworthy Systems

Divide and congruence III: From decomposition of modal formulas to preservation of stability and divergence

Authors

Wan Fokkink, Rob van Glabbeek and Bas Luttik

DATA61

Vrije Universiteit Amsterdam

Eindhoven University of Technology

UNSW Sydney

Abstract

In two earlier papers we derived congruence formats with regard to transition system specifications 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. The stability and divergence requirements that are imposed on many of the known weak semantics have so far been outside the realm of this method. Stability refers to the absence of a τ-transition. We show, using the decomposition method, how congruence formats can be relaxed for weak semantics that are stability-respecting. This relaxation for instance brings the priority operator within the range of the stability-respecting branching bisimulation format. Divergence, which refers to the presence of an infinite sequence of τ-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

  @article{Fokkink_GL_19,
    address          = {Berlin, Germany},
    author           = {Fokkink, Wan and van Glabbeek, Robert and Luttik, Bas},
    date             = {2019-10-1},
    doi              = {https://doi.org/10.1016/j.ic.2019.104435},
    editor           = {{Meyer, Roland \& Nestmann, Uwe}},
    journal          = {Information and Computation},
    keywords         = {Structural Operational Semantics; Compositionality; Congruence formats; Modal logic; Divergence;
                        Branching bisimulation},
    month            = oct,
    numpages         = {104435},
    paperurl         = {https://trustworthy.systems/publications/full_text/Fokkink_GL_19.pdf},
    publisher        = {Elsevier},
    series           = {Leibniz International Proceedings in Informatics (LIPIcs)},
    title            = {Divide and Congruence {III}: From Decomposition of Modal Formulas to Preservation of Stability and
                        Divergence},
    volume           = {268},
    year             = {2019}
  }

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