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- W4297492870 abstract "Abstract The concept of a synchronizing word is a very important notion in the theory of finite automata. We consider the associated decision problem to decide if a given DFA possesses a synchronizing word of length at most k , where k is the standard parameter. We show that this problem DFA-SW is equivalent to the problem Monoid Factorization introduced by Cai, Chen, Downey, and Fellows. Apart from the known $textsf{W}[2]$ -hardness results, we show that these problems belong to $textsf{A}[2]$ , $textsf{W}[textsf{P}],$ and $textsf{WNL}$ . This indicates that DFA-SW is not complete for any of these classes, and hence, we suggest a new parameterized complexity class $textsf{W}[textsf{Sync}]$ as a proper home for these (and more) problems. We present quite a number of problems that belong to $textsf{W}[textsf{Sync}]$ or are hard or complete for this new class." @default.
- W4297492870 created "2022-09-29" @default.
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- W4297492870 date "2022-02-01" @default.
- W4297492870 modified "2023-09-26" @default.
- W4297492870 title "Synchronizing words and monoid factorization, yielding a new parameterized complexity class?" @default.
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- W4297492870 doi "https://doi.org/10.1017/s0960129522000184" @default.
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