On the Knuth-Bendix completion for concurrent processes
We consider critical pairs for replacement systems over free partially commutative monoids. This is done in order to apply the Knuth-Bendix completion procedure to concurrent processes. We will see that there are systems which have no finite set of critical pairs, even if the system consists of one rule only. Therefore we develop a sufficient (and computable) condition such that finite replacement systems have a finite set of critical pairs if the condition is fullfilled. This condition is always satisfied in the purely free or purely commutative case of semi-Thue systems or vector-replacement systems. In fact, it generalizes (and unifies) both cases.
KeywordsCritical Pair Finite System Replacement System Concurrent Process Commutative Case
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