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Two quantum finite automata are equivalent if for any input string x the two automata accept x with equal probability. In this paper, we focus on determining the equivalence for 1-way quantum finite automata with control language (CL-1QFAs) defined by Bertoni et al and measure-many 1-way quantum finite automata (MM-1QFAs) introduced by Kondacs and Watrous.… (More)

Multi-letter quantum finite automata (QFAs) are quantum variants of the one-way multi-head finite automata (J. Hromkovič, Acta Informatica 19 (1983) 377-384). It has been shown that this new one-way QFAs (multi-letter QFAs) can accept with no error some regular languages, for example (a + b) * b, that are not acceptable by QFAs of Moore and Crutchfield [20]… (More)

Two-way quantum automata with quantum and classical states (2QCFA) were introduced by Ambainis and Watrous in 2002. In this paper we study state succinctness of 2QCFA. For any m ∈ Z + and any < 1/2, we show that: 1. there is a promise problem A eq (m) which can be solved by a 2QCFA with one-sided error in a polynomial expected running time with a constant… (More)

Generally, unitary transformations limit the computational power of quantum finite au-tomata (QFA). In this paper we study a generalized model named one-way general quantum finite automata (1gQFA), in which each symbol in the input alphabet induces a trace-preserving quantum operation, instead of a unitary transformation. Two different kinds of 1gQFA will… (More)

We show that there are quantum devices that accept all regular languages and that are exponentially more concise than deterministic finite automata (DFA). For this purpose , we introduce a new computing model of one-way quantum finite automata (1QFA), namely, one-way quantum finite automata together with classical states (1QFAC), which extends naturally… (More)

We introduce 2-way finite automata with quantum and classical states (2qcfa's). This is a variant on the 2-way quantum finite automata (2qfa) model which may be simpler to implement than unrestricted 2qfa's; the internal state of a 2qcfa may include a quantum part that may be in a (mixed) quantum state, but the tape head position is required to be… (More)

Several types of automata, such as probabilistic and quantum automata, require to work with real and complex numbers. For such automata the acceptance of an input is quantified with a probability. There are plenty of results in the literature addressing the complexity of checking the equivalence of these automata, that is, checking whether two automata… (More)