The Complexity of Finding Reset Words in Finite Automata

Details The Complexity of Finding Reset Words in Finite Automata The Complexity of Finding Reset Words in Finite Automata

2010-04-19

arxiv.org/abs/1004.3246v2

Computer Science

Formal Languages and Automata Theory

16 pages, revised version

Scientific paper

10.1007/978-3-642-15155-2_50

We study several problems related to finding reset words in deterministic finite automata. In particular, we establish that the problem of deciding whether a shortest reset word has length k is complete for the complexity class DP. This result answers a question posed by Volkov. For the search problems of finding a shortest reset word and the length of a shortest reset word, we establish membership in the complexity classes FP^NP and FP^NP[log], respectively. Moreover, we show that both these problems are hard for FP^NP[log]. Finally, we observe that computing a reset word of a given length is FNP-complete.

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