For any group G and any set A, a cellular automaton (CA) is a transformation of the configuration space A G defined via a finite memory set and a local function. Let CA(G; A) be the monoid of all CA over A G. In this paper, we investigate a generalisation of the inverse of a CA from the semigroup-theoretic perspective. An element τ ∈ CA(G; A) is von Neumann regular (or simply regular) if there ...

In this paper, the endomorphism monoid of n-prism Pr(n) is explored explicitly. It is shown that Pr(2m + 1) is endomorphism regular for any m ≥ 1 and Pr(2m) is not endomorphism regular for any m ≥ 2. Mathematics Subject Classification: 05C25, 20M20

We propose a new approach to the notion of recognition, which departs from the classical definitions by three specific features. First, it does not rely on automata. Secondly, it applies to any Boolean algebra (BA) of subsets rather than to individual subsets. Thirdly, topology is the key ingredient. We prove the existence of aminimum recognizer in a very general setting which applies in partic...

We develop the K-theory of sets with an action a pointed monoid (or scheme), analogous to modules over ring scheme). In order form localization sequences, we construct quotient category nice regular by Serre subcategory.

Let X∗ be a free monoid over an alphabet X and W be a finite language over X. Let S(W ) be the Rees quotient X∗/I(W ), where I(W ) is the ideal of X∗ consisting of all elements of X∗ that are not subwords of W . Then S(W ) is a finite monoid with zero and is called the discrete syntactic monoid of W . W is called finitely based if the monoid S(W ) is finitely based. In this paper, we give some ...

In this note we show that the nilpotence conjecture for toric varieties is true over any regular coefficient ring containing Q. In [G] we showed that for any additive submonoid M of a rational vector space with the trivial group of units and a field k with chark = 0 the multiplicative monoid N acts nilpotently on the quotient Ki(k[M ])/Ki(k) of the ith K-groups, i ≥ 0. In other words, for any s...

A graph X is said to be End-completely-regular (resp., End-inverse) if its endomorphism monoid End(X) is completely regular (resp., inverse). In this paper, we will show that if X[Y] is End-completely-regular (resp., End-inverse), then both X and Y are End-completely-regular (resp., End-inverse). We give several approaches to construct new End-completely-regular graphs by means of the lexicogra...

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's relations $mbox{$...

It is well known that varieties of rational languages are in one-to-one correspondence with varieties of finite monoids. This correspondence ofte., extends to operations on languages and on monoidc. We investigate the special case of the product of languages with counter, and describe the associated operations on monoids and varieties. R&emi. On sait que les varietes de IangagEs rationnels sont...

A zero-one language L is a regular language whose asymptotic probability converges to either zero or one. In this case, we say that L obeys the zero-one law. We prove that a regular language obeys the zero-one law if and only if its syntactic monoid has a zero element, by means of Eilenberg’s variety theoretic approach. Our proof gives an effective automata characterisation of the zero-one law ...