Operational Determinism and Fast Algorithms

Abstract

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.