Abstract. 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.
In addition, Olschewski and Ummels showed that finding the minimum reset sequence and determining the length of the minimum reset sequence are in FP NP and FP NP[log] respectively REF .
The Complexity of Finding Reset Words in Finite Automata
ArXiv
ArXiv
Computer Science