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Theoretical Computer Science - Special issue on universal machines and computations
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Journal of Computer and System Sciences - Eleventh annual conference on computational learning theory&slash;Twelfth Annual IEEE conference on computational complexity
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COCOON '00 Proceedings of the 6th Annual International Conference on Computing and Combinatorics
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FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
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This paper focuses on quantum analogues of various models of counter automata, and almost completely proves the relation between the classes of languages recognizable by bounded error quantum ones and classical deterministic ones in every model of counter automata. It is proved that (i) under some practically reasonable assumption, quantum ones are strictly stronger than deterministic ones in two-way one-counter automata, and (ii) for any fixed k, quantum ones and deterministic ones are incomparable in one-way k-counter automata.