Various languages that are accepted (or recognized) by quantum automata are discussed. For comparison, we first review the theory of classical automata. Of particular interest are the deterministic automata and the regular languages that they accept. We also consider reversible deterministic automata which accept a smaller class of languages called the reversible languages and probabilistic automata which accept a larger class. We show that reversible probabilistic automata must be deterministic. We then discuss quantum, η-quantum and η-quantum with error bound ε languages. These languages are compared with each other and with the regular and reversible languages and some of their properties are derived. It is shown that η-quantum languages with error bound ε must be reversible. We finally discuss two-way quantum automata and their languages and indicate why they are more powerful than deterministic automata.
KeywordsBoolean Algebra Regular Language Stochastic Matrix Input String Input Tape
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