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- W2053030148 abstract "Given a function p : N → [0,1] of period n, we study the minimal size (number of states) of a one-way quantum finite automaton (Iqfa) inducing the stochastic event ap + b, for real constants a>0, b≥0, a+b≤1. First of all, we relate the estimation of the minimal size to the problem of finding a minimal difference cover for a suitable subset of Z n . Then, by observing that the cardinality of a difference cover Δ for a set A ⊆ Z n , must satisfy [Formula: see text], we investigate the class of sets A admitting difference covers of cardinality exactly [Formula: see text]. We relate this problem with the efficient construction of Golomb rulers and difference sets. We design an algorithm which outputs each of the Golomb rulers (if any) of a given set in pseudo-polynomial time. As a consequence, we obtain an efficient algorithm that construct minimal difference covers for a non-trivial class of sets. Moreover, by using projective geometry arguments, we give an algorithm that, for any n=q 2 +q+1 with q prime power, constructs difference sets for Z n in quadratic time." @default.
- W2053030148 created "2016-06-24" @default.
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- W2053030148 date "2003-10-01" @default.
- W2053030148 modified "2023-09-26" @default.
- W2053030148 title "GOLOMB RULERS AND DIFFERENCE SETS FOR SUCCINCT QUANTUM AUTOMATA" @default.
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- W2053030148 doi "https://doi.org/10.1142/s0129054103002060" @default.
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