This paper investigates the word problem for inverse monoids generated by a set Γ subject to relations of the form e = f , where e and f are both idempotents in the free inverse monoid generated by Γ. It is shown that for every fixed monoid of this form the word problem can be solved both in linear time on a RAM as well as in deterministic logarithmic space, which solves an open problem of Marg...

A reversible automaton is a finite (possibly incomplete) automaton in which each letter induces a partial one-to-one map from the set of states into itself. We give four non-trivial characterizations of the languages accepted by a reversible automaton equipped with a set of initial and final states and we show that one can effectively decide whether a given rational (or regular) language can be...

We deene a new technique useful in identifying a subclass of regular languages deened on a free partially commutative monoid (regular trace languages), using equivalence and membership queries. Our algorithm extends an algorithm deened by Dana Angluin in 1987 to learn DFA's. The words of a trace language can be seen as equivalence classes of strings. We show how to extract, from a given equival...

The syntactic complexity of a regular language is the cardinality of its syntactic semigroup. The syntactic complexity of a subclass of the class of regular languages is the maximal syntactic complexity of languages in that class, taken as a function of the state complexity n of these languages. We study the syntactic complexity of prefix-, suffix-, bifix-, and factor-free regular languages. We...

A regular language L is union-free if it can be represented by a regular expression without the union operation. A union-free language is deterministic if it can be accepted by a deterministic one-cycle-freepath finite automaton; this is an automaton which has one final state and exactly one cycle-free path from any state to the final state. Jirásková and Masopust proved that the state complexi...

Every rational number p q defines a rational base numeration system in which every integer has a unique finite representation, up to leading zeroes. This work is a contribution to the study of the set of the representations of integers. This prefix-closed subset of the free monoid is naturally represented as a highly non-regular tree. Its nodes are the integers, its edges bear labels taken in {...

We consider varieties of tree languages which are not restricted to a fixed ranked alphabet, varieties of finite algebras that contain algebras of all finite types, and a matching notion of varieties of congruences. A variety theorem that yields isomorphisms between the lattices formed by these three types of varieties is proved. To achieve this, some basic universal algebra is suitably general...

We use syntactic monoid methods, together with an enhanced pumping lemma, to investigate the structure of splicing languages. We obtain an algorithm for deciding whether a regular language is a reflexive splicing language, but the general question remains open.

We introduce the notion of regular cost functions: a quantitative extension to the standard theory of regular languages. We provide equivalent characterisations of this notion by means of automata (extending the nested distance desert automata of Kirsten), of history-deterministic automata (history-determinism is a weakening of the standard notion of determinism, that replaces it in this contex...

We present Stamina, a tool solving three algorithmic problems in automata theory. First, compute the star height of a regular language, i.e. the minimal number of nested Kleene stars needed for expressing the language with a complement-free regular expression. Second, decide limitedness for regular cost functions. Third, decide whether a probabilistic leaktight automaton has value 1, i.e. wheth...