Quantum Finite One-Counter Automata
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Kravtsev introduced 1-way quantum 1-counter automata (1Q1CAs), and showed that several non-context-free languages can be recognized by bounded error 1Q1CAs. In this paper, we first show that all of these non-context-free languages can be also recognized by bounded error 1PR1CAs (and so 1Q1CAs). Moreover, the accepting probability of each of these 1PR1CAs is strictly greater than, or at least equal to, that of corresponding Kravtsev's original 1Q1CA. Second, we show that there exists a bounded error 1PR1CA (and so 1Q1CA) which recognizes {a1na2n...akn}, for each k ≥ 2. We also show that, in a quantum case, we can improve the accepting probability in a strict sense by using quantum interference. Third, we state the relation between 1-way deterministic 1- counter automata (1D1CAs) and 1Q1CAs. On one hand, all of above mentioned languages cannot be recognized by 1D1CAs because they are non-context-free. On the other hand, we show that a regular language {{a,b*a} cannot be recognized by bounded error 1Q1CAs.