Received (Day Month Year)

Accepted (Day Month Year) Communicated by (xxxxxxxxxx) We study a novel representation of semiautomata, which is motivated by the method of trace-assertion specifications of software modules. Each state of the semiautomaton is represented by an arbitrary word leading to that state, the canonical word. The transi-tions of the semiautomaton give rise to a right congruence, the state-equivalence, on the set of input words of the semiautomaton: two words are state-equivalent if and only if they lead to the same state. We present a simple algorithm for finding a set of genera-tors for state-equivalence. Directly from this set of generators, we construct a confluent prefix-rewriting system which permits us to transform any word to its canonical repre-sentative. In general, the rewriting system may allow infinite derivations. To address this issue, we impose the condition of prefix-continuity on the set of canonical words. A set is prefix-continuous if, whenever a word w and a prefix u of w are in the set, then all the prefixes of w longer than u are also in the set. Prefix-continuous sets include prefix-free and prefix-closed sets as special cases. We prove that the rewriting system is Noetherian if and only if the set of canonical words is prefix-continuous. Furthermore, if the set of canonical words is prefix-continuous, then the set of rewriting rules is irredundant. W