A deterministic finite automaton is synchronizing if there exists a word that sends all states of the automaton to the same state. Černý conjectured in 1964 that a synchronizing automaton with n states has a synchronizing word of length at most (n− 1). We introduce the notion of aperiodically 1−contracting automata and prove that in these automata all subsets of the state set are reachable, so ...

Stochastic deterministic finite automata have been introduced and are used in a variety of settings. We report here a number of results concerning the learnability of these finite state machines. In the setting of identification in the limit with probability one, we prove that stochastic deterministic finite automata cannot be identified from only a polynomial quantity of data. If concerned wit...

The power of weighted nite automata to describe very complex images was widely studied, see [5, 6, 7]. Finite automata can be also used as an e ective tool for compression of twodimensional images. There are some software packages using this type of compression, see [12, 6]. We consider the complexity of some pattern-matching problems for two-dimensional images which are highly compressed using...

An algorithm is proposed that constructs a failure deterministic finite automaton in lockstep with the construction of a languageequivalent deterministic finite automaton. The states of both automata are assumed to be predefined and the failure deterministic finite automaton’s symbol and failure transitions are randomised. It is guaranteed that the latter remains free of divergent failure cycle...

A word is called a reset word for a deterministic finite automaton if it maps all the states of the automaton to a unique state. Deciding about the existence of a reset word of a given maximum length for a given automaton is known to be an NP-complete problem. We prove that it remains NP-complete even if restricted to Eulerian automata with binary alphabets, as it has been conjectured by Martyu...

The words separation problem, originally formulated by Goralcik and Koubek (1986), is stated as follows. Let Sep(n) be the minimum number such that for any two words of length 6 n there is a deterministic finite automaton with Sep(n) states, accepting exactly one of them. The problem is to find the asymptotics of the function Sep. This problem is inverse to finding the asymptotics of the length...

A deterministic finite automaton is synchronizing if there exists a word that sends all states of the automaton to the same state. Černý conjectured in 1964 that a synchronizing automaton with n states has a synchronizing word of length at most (n− 1)2. We introduce the notion of aperiodically 1-contracting automata and prove that in these automata all subsets of the state set are reachable, so...

In this work we study Good-For-Games (GFG) automata over ω-words: non-deterministic automata where the non-determinism can be resolved by a strategy depending only on the prefix of the ω-word read so far. These automata retain some advantages of determinism: they can be composed with games and trees in a sound way, and inclusion LpAq … LpBq can be reduced to a parity game over A B if A is GFG. ...

We prove that any local automaton is contained in a complete one. The proof uses Nasu’s masking lemma. We use the same technique to give a new proof that any weakly deterministic irreducible automaton is contained in a complete one.

We consider a deterministic finite automaton which accepts all subsequences of a set of texts, called subsequence automaton. We show an online algorithm for constructing subsequence automaton for a set of texts. It runs in O(|Σ|(m+ k) +N) time using O(|Σ|m) space, where |Σ| is the size of alphabet, m is the size of the resulting subsequence automaton, k is the number of texts, and N is the tota...