This paper deals with decision problems related to the star problem in trace monoids, which means to determine whether the iteration of a recognizable trace language is recognizable. Due to a theorem by Richomme from 1994 30, 31], we know that the Star Problem is decidable in trace monoids which do not contain a C4-submonoid. The C4 is (isomorphic to) the Cartesian Product of two free monoids o...

The semidirect product of two groups is a natural generalization of the direct product of two groups in that the requirement that both factors be normal in the product is replaced by the weaker requirement that only one of the factors be normal in the product. The Zappa-Szép product of two groups is a natural generalization of the semidirect product of two groups in that neither factor is requi...

Finite permutation groups can be considered as building blocks of finite transformation monoids. Indeed, by the Krohn-Rhodes Theorem, any finite transformation monoid divides a semidirect product of permutation groups and three element transformation monoids. Given a transformation monoid M on a finite set, defined by a finite set of generators, it is in general non-trivial to obtain a descript...

Starting from Boolean algebras of languages closed under quotients and using duality theoretic insights, we derive the notion of Boolean spaces with internal monoids as recognisers for arbitrary formal languages of finite words over finite alphabets. This leads to recognisers and syntactic spaces equivalent to those proposed in [8], albeit in a setting that is well-suited for applying existing ...

Abstract In the classical theory of regular languages, concept recognition by profinite monoids is an important tool. Beyond regularity, Boolean spaces with internal (BiMs) were recently proposed as a generalization. On other hand, fragments logic defining languages can be studied inductively via so-called “Substitution Principle.” this paper, we make logical underpinnings principle explicit an...

Abstract This article studies the properties of word-hyperbolic semigroups and monoids, that is, those having context-free multiplication tables with respect to a regular combing, as defined by Duncan Gilman [‘Word hyperbolic semigroups’, Math. Proc. Cambridge Philos. Soc. 136 (3) (2004), 513–524]. In particular, preservation word-hyperbolicity under taking free products is considered. Under mi...

Given a direct product of monoids M = A∗ ×Nm where A is finite and N is the additive monoid of nonnegative integers, the following problem is recursively decidable: given two rational subsests of M , does there exist a recognizable subset which includes one of the subsets and excludes the other.

In this paper, we give the properties of tensor product and study the relationship between Hom functors and left (right) exact sequences in FS-Act. Also, we get some necessary conditions for equivalence of two fuzzy Sacts category. Moreover, we prove that two monoids S and T are Morita equivalent if and only if FS-Act and FT -Act are equivalent.

‎there is a flatness property of acts over monoids called condition $(pwp)$ which‎, ‎so far‎, ‎has received‎ ‎much attention‎. ‎in this paper‎, ‎we introduce condition gp-$(p)$‎, ‎which is a generalization of condition $(pwp)$‎. ‎firstly‎, ‎some  characterizations of monoids by condition gp-$(p)$ of their‎ ‎(cyclic‎, ‎rees factor) acts are given‎, ‎and many known results are generalized‎. ‎more...

AmonoidM is called surjunctive if every injective cellular automata with finite alphabet over M is surjective. We show that all finite monoids, all finitely generated commutative monoids, all cancellative commutative monoids, all residually finite monoids, all finitely generated linear monoids, and all cancellative one-sided amenable monoids are surjunctive. We also prove that every limit of ma...