We prove that there exist a dimension group G whose positive cone is not isomorphic to the dimension monoid DimL of any lattice L. The dimension group G has an order-unit, and can be taken of any cardinality greater than or equal to א2. As to determining the positive cones of dimension groups in the range of the Dim functor, the א2 bound is optimal. This solves negatively the problem, raised by...

We study the classes of languages defined by valence automata with rational target sets (or equivalently, regular valence grammars with rational target sets), where the valence monoid is drawn from the important class of polycyclic monoids. We show that for polycyclic monoids of rank 2 or more, such automata accept exactly the context-free languages. For the polycyclic monoid of rank 1 (that is...

Functional MSO transductions, deterministic two-way transducers, as well as streaming string transducers are all equivalent models for regular functions. In this paper, we show that every regular function, either on finite words or on infinite words, captured by a deterministic two-way transducer, can be described with a regular transducer expression (RTE). For infinite words, the transducer us...

We study sources of isomorphisms of additive cellular automata on finite groups (called index-group). It is shown that many isomorphisms (called regular) of automata are reducible to the isomorphisms of underlying algebraic structures (such as the index-group, monoid of automata rules, and its subgroup of reversible elements). However for some groups there exist not regular automata isomorphism...

AUTOMATE is a package for symbolic computation on nite automata, extended rational expressions and nite semigroups. On the one hand, it enables one to compute the deterministic minimal automaton of the language represented by a rational expression or given by its table. On the other hand, given the transition table of a deterministic automaton, AUTOMATE computes the associated transition monoid...

We extend the notion of a purely infinite simple C*-algebra to the context of unital rings, and we study its basic properties, specially those related to K-Theory. For instance, if R is a purely infinite simple ring, then K0(R) + = K0(R), the monoid of isomorphism classes of finitely generated projective R-modules is isomorphic to the monoid obtained from K0(R) by adjoining a new zero element, ...

Let M be an irreducible normal algebraic monoid with unit group G. It is known that G admits a Rosenlicht decomposition, G = GantGaff ∼= (Gant ×Gaff )/Gaff ∩Gant, where Gant is the maximal anti-affine subgroup of G, and Gaff the maximal normal connected affine subgroup of G. In this paper we show that this decomposition extends to a decomposition M = GantMaff ∼= Gant∗Gaff∩GantMaff , whereMaff i...

The main goal of this work is the investigation of some properties of co-regular languages. In many applications it is important to handle innnite sets of terms. We represent two equivalent formalisms for nite deened innnite sets of term substitutions which are leading to co-regular languages. As it will be proved later the co-regular languages are monoidic homomorphical images of regular langu...

the aim of this paper is to study semigroups possessing $e$-regular elements, where an element $a$ of a semigroup $s$ is {em $e$-regular} if $a$ has an inverse $a^circ$ such that $aa^circ,a^circ a$ lie in $ esubseteq e(s)$. where $s$ possesses `enough' (in a precisely defined way) $e$-regular elements, analogues of green's lemmas and even of green's theorem hold, where green&apos...