Operational Determinism and Fast Algorithms

  • Henri Hansen
  • Antti Valmari
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4137)


The main contribution of this work is a fast algorithm for checking whether a labelled transition system (LTS) is operationally deterministic. Operational determinism is a condition on the LTS designed to capture the notion of “deterministic behaviour” without ruling out invisible actions and divergence, and without strictly devoting oneself to any single process-algebraic semantics. Indeed, we show that in the case of operationally deterministic LTSs, all divergence-sensitive equivalences between divergence-sensitive branching bisimilarity and trace + divergence trace equivalence collapse to the same equivalence. The running time of the algorithm is linear except a term that, roughly speaking, grows as slowly as Ackermann’s function grows quickly. If the original LTS is operationally deterministic, the algorithm produces as a by-product a structurally deterministic LTS that is divergence-sensitive branching bisimilar to the original one. This LTS can be minimised like a deterministic finite automaton. The overall approach is so cheap that it makes almost always sense to first try it and revert to a semantics-specific reduction or minimisation algorithm only if the LTS proves operationally nondeterministic.


Fast Algorithm Label Transition System Structural Determinism Bottom State Divergence Trace 
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

  • Henri Hansen
    • 1
  • Antti Valmari
    • 1
  1. 1.Institute of Software SystemsTampere University of TechnologyTampereFinland

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