The complexity of testing the equivalence of transition sequences
By [Best 89] and [Best, Devillers 88] a semantics for place/transition nets has been defined on equivalence classes of firing sequences induced by the exchange relation (two transitions can be exchanged if they are concurrently enabled). This semantics preserves the causal dependences between transitions. For the equivalence relation we show: Given a place/transition net N and two firing sequences u, v ∈ F(N), the question u ≡ v is NP-hard. For a corresponding equivalence relation on processes (or partially ordered multisets) the test of equivalence will remain NP-hard.
KeywordsCausality/partial order theory of concurrency Analysis and synthesis structure and behaviour of nets Net-based semantical logical and algebraic calculi
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