The aim of the article is to present two algebraic tools (the representable transductions and the relational morphisms) that have been used in the past decade to study operations on recognizable languages. This study reserves a few surprises. Indeed, both concepts were originally introduced for other purposes : representable transductions are a formalization of automata with output and have bee...

In this dissertation we classify the metabelian groups arising from a restricted class of invertible synchronous automata over a binary alphabet. We give faithful, self-similar actions of Heisenberg groups and upper triangular matrix groups. We introduce a new class of semigroups given by a restricted class of asynchronous automata. We call these semigroups " expanding automaton semigroups ". W...

Automatic presentations, also called FA-presentations, were introduced to extend finite model theory to infinite structures whilst retaining the solubility of interesting decision problems. A particular focus of research has been the classification of those structures of some species that admit automatic presentations. Whilst some successes have been obtained, this appears to be a difficult pro...

ON NON-EMPTY WORDS IN FINITE AUTOMATA PÁL DÖMÖSI, CHRYSTOPHER L. NEHANIV, AND JOHN L. RHODES ABSTRACT. This paper relates classes of finite automata under various feedback products to some well-known pseudovarieties of finite semigroups via a study of their irreducible divisors (in the sense of Krohn-Rhodes). In particular, this serves to relate some classical results of Krohn, Rhodes, Stiffler...

In this paper, we prove existence and controllability results for first and second order semilinear neutral functional differential inclusions with finite or infinite delay in Banach spaces, with nonlocal conditions. Our theory makes use of analytic semigroups and fractional powers of closed operators, integrated semigroups and cosine families.

Semigroups in which every principal congruence is of finite index are studied in this paper.

For applications in algebraic geometric codes, an explicit description of bases of Riemann-Roch spaces of divisors on function fields over finite fields is needed. We give an algorithm to compute such bases for one point divisors, and Weierstrass semigroups over an optimal tower of function fields. We also explicitly compute Weierstrass semigroups till level eight. MSC2010 Subject Classificatio...

J. Rhodes asked during the Chico conference in 1986 for the calculation of joins of semigroup pseudovarieties. This paper proves that the join J∨V of the pseudovariety J of J -trivial semigroups and of any 2-strongly decidable pseudovariety V of completely regular semigroups is decidable. This problem was proposed by the first author for V = G, the pseudovariety of finite groups.

Group theory and semigroup theory have developed in somewhat different directions in the past several decades. While Cayley’s theorem enables us to view groups as groups of permutations of some set, the analogous result in semigroup theory represents semigroups as semigroups of functions from a set to itself. Of course both group theory and semigroup theory have developed significantly beyond t...