The concept of q , -fuzzy ternary subsemigroup (left, right, lateral, quasi-, bi-) ideal of a ternary semigroup is introduced and several related properties are investigated. We give some characterizations of regular and weakly regular ternary semigroups by q , -fuzzy left (right, lateral) ideals, q , -fuzzy quasi-ideals and q , -fuzzy bi-(generalized bi-) ideals.

A nitely presented monoid has a decidable word problem if and only if it can be presented by some left-recursive convergent string-rewriting system if and only if it has a recursive cross-section. However, context-free cross-sections or even regular cross-sections do not suuce. This is shown by presenting examples of nitely presented monoids with decidable word problems that do not admit regula...

We consider random walks on idempotent semigroups, called Left Regular Bands, satisfying the relation xyx = xy for any two elements x and y of the semigroup. We give an alternating upper bound for the total variation distance of a random walk on a Left Regular Band semigroup, improving the previous bound by Brown and Diaconis.

Abstract In this paper, we have introduced anti fuzzy quasi-ideals, anti fuzzy bi-(generalized bi-) ideals and anti fuzzy left (right, two-sided) ideals in LA-semigroup. Further we have characterized an intra-regular LA-semigroup by the properties of their anti fuzzy left (right, two-sided) ideals, anti fuzzy bi(generalized bi-)ideals, anti fuzzy interior ideals and anti fuzzy quasi-ideals. Fur...

In this paper,The concept of a (∈,∈ ∨q)-fuzzy ideal in an ordered Abel-Grassmann groupoid is introduced. In partcicular, left regular ordered Abel-Grassmann groupoids are characterized by using the (∈ ,∈ ∨q)-fuzzy ideals.

We follow language theoretic approach to synchronizing automata and Černý’s conjecture initiated in a series of recent papers. We find a precise lower bound for the reset complexity of a principal ideal languages. Also we show a strict connection between principal left ideals and synchronizing automata. We characterize regular languages whose minimal deterministic finite automaton is synchroniz...

An arrangement of curves in the real plane divides it into a collection of faces. Already in the case of line arrangements, this collection can be given a structure of a left regular band and one can ask whether the same is possible for other arrangements. In this paper, we try to answer this question for the simplest generalization of line arrangements, that is, conic–line arrangements. Invest...

This papers introduces several binary scalar multiplication algorithms with applications to cryptography. Remarkably, the proposed algorithms regularly repeat the same pattern when evaluating a scalar multiplication in an (additively written) abelian group. Furthermore, they are generic and feature the following properties: – no dummy operation is involved; – no precomputation nor prior recodin...

We consider the problem of non-adaptive group testing of N items out of which K or less items are known to be defective. We propose a testing scheme based on left-andright-regular sparse-graph codes and a simple iterative decoder. We show that for any arbitrarily small ǫ > 0 our scheme requires only m = cǫK log c1N K tests to recover (1− ǫ) fraction of the defective items with high probability ...

Each context-free grammar can be transformed to a context-free grammar in Greibach normal form, that is, a con text-free grammar where each right-hand side of a prorfuction begins with a terminal symbol and the remainder of the right-hand side consists of nonterminal symbols. In this short paper we show that for a left-regular grammar G we can obtain a right-regular grammar G’ (which is by defi...