Upper Bounds on the Size of One-Way Quantum Finite Automata
ICTCS '01 Proceedings of the 7th Italian Conference on Theoretical Computer Science
On Computational Power of Quantum Branching Programs
FCT '01 Proceedings of the 13th International Symposium on Fundamentals of Computation Theory
Quantum computing: 1-way quantum automata
DLT'03 Proceedings of the 7th international conference on Developments in language theory
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The 2-way quantum finite automaton introduced by Kondacs and Watrous\cite{KoWa97} can accept non-regular languages with bounded error in polynomial time. If we restrict the head of the automaton to moving classically and to moving only in one direction, the acceptance power of this 1-way quantum finite automaton is reduced to a proper subset of the regular languages. In this paper we study two different models of 1-way quantum finite automata. The first model, termed measure-once quantum finite automata, was introduced by Moore and Crutchfield\cite{MoCr98}, and the second model, termed measure-many quantum finite automata, was introduced by Kondacs and Watrous\cite{KoWa97}. We characterize the measure-once model when it is restricted to accepting with bounded error and show that, without that restriction, it can solve the word problem over the free group. We also show that it can be simulated by a probabilistic finite automaton and describe an algorithm that determines if two measure-once automata are equivalent. We prove several closure properties of the classes of languages accepted by measure-many automata, including inverse homomorphisms, and provide a new necessary condition for a language to be accepted by the measure-many model with bounded error. Finally, we show that piecewise testable languages can be accepted with bounded error by a measure-many quantum finite automaton, in the process introducing new construction techniques for quantum automata.