Let L(M) be the (factorial) language avoiding a given anti-factorial language M. We design an automaton accepting L(M) and built from the language M. The construction is eeective if M is nite. If M is the set of minimal forbidden words of a single word v, the automaton turns out to be the factor automaton of v (the minimal automaton accepting the set of factors of v). We also give an algorithm ...

A linear recurrence relation is derived for the number of unlabelled initially connected acyclic automata. The coefficients of this relation are determined by another, alternating, recurrence relation. The latter determines, in particular, the number of acyclic automata with labelled states. Certain simple enumerative techniques developed by the author for counting initially connected automata ...

Tree automata modulo associativity and commutativity axioms, called AC tree automata, accept trees by iterating the transition modulo equational reasoning. The class of languages accepted by monotone AC tree automata is known to include the solution set of the inequality x × y > z, which implies that the class properly includes the AC closure of regular tree languages. In the paper, we characte...

We analyze the properties of probabilistic reversible decide-and-halt automata (DHPRA) and show that there is a strong relationship between DH-PRA and 1-way quantum automata. We show that a general class of regular languages is not recognizable by DHPRA by proving that two ‘‘forbidden’’ constructions in minimal deterministic automata correspond to languages not recognizable by DH-PRA. The shown...

In the paper we continue studying essential inputs of trees and automata initiated in [10]. We distinguish the behavior of the essential inputs of trees and essential variables for discrete functions. Strongly essential inputs of trees are introduced too. It is proved that if a tree and an automaton have at least two essential inputs then they have at least one strongly essential input. A minim...

A cover-automaton A of a "nite language L⊆ ∗ is a "nite deterministic automaton (DFA) that accepts all words in L and possibly other words that are longer than any word in L. A minimal deterministic "nite cover automaton (DFCA) of a "nite language L usually has a smaller size than a minimal DFA that accept L. Thus, cover automata can be used to reduce the size of the representations of "nite la...

A prominent learning algorithm is Angluin’s L∗ algorithm, which allows to learn a minimal deterministic automaton using so-called membership and equivalence queries addressed to a teacher. In many applications, however, a teacher might be unable to answer some of the membership queries because parts of the object to learn are not completely specified, not observable, it is too expensive to reso...

A cover-automaton A of a finite language L ⊆ Σ∗ is a finite automaton that accepts all words in L and possibly other words that are longer than any word in L. A minimal deterministic cover automaton of a finite language L usually has a smaller size than a minimal DFA that accept L. Thus, cover automata can be used to reduce the size of the representations of finite languages in practice. In thi...

Cayley graphs considered as language recognisers are as powerful as the more general finite state automata. This paper applies Cayley graphs to define a class of automata and describe minimal automata of this type, all their congruences and the Nerode equivalence of states. Throughout, the word graph means a finite directed graph without multiple edges but possibly with loops, and D = (V,E) is ...

We improve on an existing [P.A. Abdulla, J. Högberg, L. Kaati. Bisimulation Minimization of Tree Automata. Int. J. Found. Comput. Sci. 18(4): 699–713, 2007] bisimulation minimization algorithm for finite-state tree automata by introducing backward and forward bisimulation and developing minimization algorithms for them. Minimization via forward bisimulation is also effective on deterministic tr...