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- W1522643802 abstract "Two quantum finite automata are equivalent if for all input string $omega$ over the input alphabet the two automata accept $omega$ with equal probability. In [Theoret. Comput. Sci. 410 (2009) 3006-3017], it was shown that a $k_1$-letter QFA $mathcal{A}_1$ and a $k_2$-letter QFA $mathcal{A}_2$ over $Sigma={sigma}$, are equivalent if and only if they are $(n_1+n_2)^4+k-1$-equivalent where $n_i$ is the number of states of $mathcal{A}_i$, $i=1,2$, and $k=max{k_1,k_2}$. In this letter, we improve the above upper-bound to $(n_1^2+n_2^2-1)+k$. This also answers an open problem of Qiu et al. [Acta Informatica 48 (2011) 271-290]. Further, we show that, in the case of $Sigma={sigma_1,...,sigma_t}$ with $2leq t<infty$, there exists an integer $z$ such that $mathcal{A}_1$ and $mathcal{A}_2$ are equivalent if and only if they satisfy $z$-equivalent." @default.
- W1522643802 created "2016-06-24" @default.
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- W1522643802 date "2011-06-26" @default.
- W1522643802 modified "2023-10-17" @default.
- W1522643802 title "Some results on equivalence of multi-letter quantum finite automata" @default.
- W1522643802 doi "https://doi.org/10.48550/arxiv.1106.5223" @default.
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