where both terms consist of two alternating letters and have the same length. First investigated by J.Tits in the late 1960s [2], and then in [3] and [11], these groups remain incompletely understood, with many open questions, including the decidability of the Word Problem in the general case [6]. The only well understood case is the one of spherical type, which is the case when the associated ...

We consider the value 1 problem for probabilistic automata over finite words. This problem is known to be undecidable. However, different algorithms have been proposed to partially solve it. The aim of this paper is to prove that one such algorithm, called the Markov Monoid algorithm, is optimal. To this end, we develop a profinite theory for probabilistic automata. This new framework gives a t...

By substantial changes and corrections in Demushkin’s old paper the essentially final positive answer to the isomorphism problem for monoid rings of submonoids of Z’ is obtained. This means that the underlying monoid is shown to be determined (up to isomorphism) by the corresponding monoid ring. Thereafter the positive answer to the analogous question for the ‘dual’ objects descrete Hodge algeb...

Based on different concepts to obtain a finer notion of language recognition via finite monoids we develop an algebraic structure called typed monoid. This leads to an algebraic description of regular and non regular languages. We obtain for each language a unique minimal recognizing typed monoid, the typed syntactic monoid. We prove an Eilenberg-like theorem for varieties of typed monoids as w...

We extend the result obtained in [3] to every Renner monoid: we provide Renner monoids with a monoid presentation and we introduce a length function which extends the Coxeter length function and which behaves nicely.

The aim of this paper is to extend the truth value table oflattice-valued convergence spaces to a more general case andthen to use it to introduce and study the quantale-valued fuzzy Scotttopology in fuzzy domain theory. Let $(L,*,varepsilon)$ be acommutative unital quantale and let $otimes$ be a binary operationon $L$ which is distributive over nonempty subsets. The quadruple$(L,*,otimes,varep...

An algebra M = (M ; ,∨,∧,→, 0, 1) of type 〈2, 2, 2, 2, 0, 0〉 is called a bounded commutative R`-monoid iff (i) (M ; , 1) is a commutative monoid, (ii) (M ;∨,∧, 0, 1) is a bounded lattice, and (iii) x y ≤ z ⇐⇒ x ≤ y → z, (iv) x (x → y) = x ∧ y, for each x, y, z ∈ M . In the sequel, by an R`-monoid we will mean a bounded commutative R`-monoid. (Note that bounded commutative R`-monoids are just bo...

It is known that the problem of determining consistency of a finite system of equations in a free group or a free monoid is decidable, but the corresponding problem for systems of equations in a free inverse monoid of rank at least two is undecidable. Any solution to a system of equations in a free inverse monoid induces a solution to the corresponding system of equations in the associated free...

It is well-known that many decision problems are undecidable in general for the class of all nite monoid-presentations. Here we consider the question of which of these problems remain undecidable even for very restricted classes of nite monoid-presentations. The restrictions we are interested in concern the number of generators admitted and the condition that each nite monoid-presentation consi...

We show that any normal algebraic monoid is an extension of an abelian variety by a normal affine algebraic monoid. This extends (and builds on) Chevalley’s structure theorem for algebraic groups.