J an 2 01 2 Another approach to the equivalence of measure-many one-way quantum finite automata and its application ✩

In this paper, we present a much simpler, direct and elegant approach to the equivalence problem of measure many one-way quantum finite automata (MM1QFAs). The approach is essentially generalized from the work of Carlyle [J. Math. Anal. Appl. 7 (1963) 167-175]. Namely, we reduce the equivalence problem of MM-1QFAs to that of two (initial) vectors. As an application of the approach, we utilize it to address the equivalence problem of Enhanced one-way quantum finite automata (E-1QFAs) introduced by Nayak [Proceedings of the 40th Annual IEEE Symposium on Foundations of Computer Science, 1999, pp. 369-376]. We prove that two E-1QFAs A1 and A2 over Σ are equivalence if and only if they are n1 + n 2 2 − 1-equivalent where n1 and n2 are the numbers of states in A1 and A2, respectively.

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