Some Remarks on Definability of Process Graphs

  • Clemens Grabmayer
  • Jan Willem Klop
  • Bas Luttik
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4137)


We propose the notions of “density” and “connectivity” of infinite process graphs and investigate them in the context of the well-known process algebras BPA and BPP. For a process graph G, the density function in a state s maps a natural number n to the number of states of G with distance less or equal to n from s. The connectivity of a process graph G in a state s is a measure for how many different ways “of going from s to infinity” exist in G.

For BPA-graphs we discuss some tentative findings about the notions density and connectivity, and indicate how they can be used to establish some non-definability results, stating that certain process graphs are not BPA-graphs, and stronger, not even BPA-definable. For BPP-graphs, which are associated with processes from the class of Basic Parallel Processes (BPP), we prove that their densities are at most polynomial. And we use this fact for showing that the paradigmatic process Queue is not expressible in BPP.


Transition Graph Pattern Graph Process Algebra Large State Space Exponential Density 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Clemens Grabmayer
    • 1
  • Jan Willem Klop
    • 2
  • Bas Luttik
    • 3
  1. 1.Department of Computer ScienceVrije Universiteit AmsterdamHV AmsterdamThe Netherlands
  2. 2.Department of Computer Science, Vrije Universiteit AmsterdamVrije Universiteit and CWI Amsterdam, and Radboud Universiteit NijmegenHV AmsterdamThe Netherlands
  3. 3.Department of Mathematics and Computer Science, TU/eTechnische Universiteit Eindhoven, and CWI AmsterdamMB EindhovenThe Netherlands

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