Transformation and Refinement of Rigid Structures

  • Vincent Danos
  • Reiko Heckel
  • Pawel Sobocinski
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8571)

Abstract

Stochastic rule-based models of networks and biological systems are hard to construct and analyse. Refinements help to produce systems at the right level of abstraction, enable analysis techniques and mappings to other formalisms. Rigidity is a property of graphs introduced in Kappa to support stochastic refinement, allowing to preserve the number of matches for rules in the refined system. In this paper: 1) we propose a notion of rigidity in an axiomatic setting based on adhesive categories; 2) we show how the rewriting of rigid structures can be defined systematically by requiring matches to be open maps reflecting structural features which ensure that rigidity is preserved; and 3) we obtain in our setting a notion of refinement which generalises that in Kappa, and allows a rule to be partitioned into a set of rules which are collectively equivalent to the original. We illustrate our approach with an example of a social network with dynamic topology.

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Vincent Danos
    • 1
  • Reiko Heckel
    • 2
  • Pawel Sobocinski
    • 3
  1. 1.School of InformaticsUniversity of EdinburghUK
  2. 2.Department of Computer ScienceUniversity of LeicesterUK
  3. 3.Electronics and Computer ScienceUniversity of SouthamptonUK

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