Abstract
We show that, for any stochastic event p of period n, there exists a measure-once one-way quantum finite automaton (1qfa) with at most \( 2\sqrt {6n} + 25 \) states inducing the event ap + b, for constants a > 0, b ≤ 0, satisfying a + b ≤ 1. This fact is proved by designing an algorithm which constructs the desired 1qfa in polynomial time. As a consequence, we get that any periodic language of period n can be accepted with isolated cut point by a 1qfa with no more than \( 2\sqrt {6n} + 26 \) states. Our results give added evidence of the strength of measure-once 1qfa’s with respect to classical automata.
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Mereghetti, C., Palano, B. (2001). Upper Bounds on the Size of One-Way Quantum Finite Automata. In: Theoretical Computer Science. ICTCS 2001. Lecture Notes in Computer Science, vol 2202. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45446-2_8
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DOI: https://doi.org/10.1007/3-540-45446-2_8
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