Abstract
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 one-rule systems which have no finite set of critical pairs. Therefore we develop a sufficient (and computable) condition such that finite trace replacement systems have a finite set of critical pairs. This condition is always satisfied in the purely free case of semi-Thue systems or purely commutative case of vector replacement systems. In fact, it generalizes (and unifies) both cases. We will give examples of how one can use this generalization.
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