A cover automaton of a finite language L is a finite automaton that accepts all words in L and possibly other words that are longer than any word in L. An algorithm for constructing a minimal cover automaton of a finite language L is given in a recent paper. This paper goes a step further by proposing a procedure for constructing all minimal cover automata of a given finite language L. The conc...

In Ufnarovski (1989), the concept of automaton algebras is introduced. These are quotients of the non-commutative polynomial ring where the defining ideal allows some Gröbner basis with a regular set of leading words. However, nothing is reflected concerning the whole structure of the Gröbner basis (except of course for monomial algebras). In this paper we introduce the concept of regular Gröbn...

The problem of computing the edit-distance between a string and a finite automaton arises in a variety of applications in computational biology, text processing, and speech recognition. This paper presents linear-space algorithms for computing the edit-distance between a string and an arbitrary weighted automaton over the tropical semiring, or an unambiguous weighted automaton over an arbitrary...

Some results from [2], [5], [6] are generalized for nite automata over arbitrary groups. The accepting power is smaller when abelian groups are considered, in comparison with the non-abelian groups. We prove that this is due to the commutativity. Each language accepted by a nite automaton over an abelian group is actually a unordered vector language. Finally, deterministic nite automata over gr...

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 ...

We present a new algorithm to construct a (generalized) deterministic Rabin automaton for an LTL formula φ. The automaton is the product of a co-Büchi automaton for φ and an array of Rabin automata, one for each G-subformula of φ. The Rabin automaton for Gψ is in charge of recognizing whether FGψ holds. This information is passed to the co-Büchi automaton that decides on acceptance. As opposed ...

To oli showed that every cellular automaton of an arbitrary dimension d can be embedded into a reversible cellular automaton of dimension d+1. He asked \whether an arbitrary cellular automaton can be embedded in a reversible one having the same number of dimensions" and conjectured that this is not possible. We show that his conjecture is true. Even if one imposes only a weak, natural condition...

The suffix automaton (resp. factor automaton) of a finite word w is the minimal deterministic automaton recognizing the set of suffixes (resp. factors) of w. We study the relationships between the structure of the suffix and factor automata and classical combinatorial parameters related to the special factors of w. We derive formulae for the number of states of these automata.We also characteri...

Given a non-deterministic timed automaton with silent transitions (eNTA), we show that after an initial stage it becomes timeperiodic. After computing the periodic parameters, we construct a finite almost periodic augmented region automaton, which includes a clock measuring the global time. In the next step we construct the timestamp of the automaton: the union of all its observable timed trace...

We consider blind, deterministic, finite automata equipped with a register which stores an element of a given monoid, and which is modified by right multiplication by monoid elements. We show that, for monoids M drawn from a large class including groups, such an automaton accepts the word problem of a group H if and only if H has a finite index subgroup which embeds in M . In the case that M is...