Finite Semigroups of Constant Rank, and the five Basic State Machine types

Restricted cascade and wreath products of fuzzy finite switchboard state machines

A finite switchboard state machine is a specialized finite state machine. It is built by binding the concepts of switching state machines and commutative state machines. The main purpose of this paper is to give a specific algorithm for fuzzy finite switchboard state machine and also, investigates the concepts of switching relation, covering, restricted cascade products and wreath products of f...

Decidability and Tameness in the Theory of Finite Semigroups

Deciding Word Problems of Semigroups using Finite State Automata

We explore natural classes of finitely generated semigroups that have word problem decidable by synchronous or asynchronous two-tape finite state automata. Synchronous two-tape automata decide regular word problems and asynchronous automata decide rational word problems. We argue that asynchronous two-tape automata are a more suitable choice than synchronous two-tape automata and show that the ...

Finite Aperiodic Semigroups with Commuting Idempotents and Generalizations

Among the most important and intensively studied classes of semigroups are finite semigroups, regular semigroups and inverse semigroups. Finite semigroups arise as syntactic semigroups of regular languages and as transition semigroups of finite automata. This connection has lead to a large and deep literature on classifying regular languages by means of algebraic properties of their correspondi...

Classification of Monogenic Ternary Semigroups

The aim of this paper is to classify all monogenic ternary semigroups, up to isomorphism. We divide them to two groups: finite and infinite. We show that every infinite monogenic ternary semigroup is isomorphic to the ternary semigroup O, the odd positive integers with ordinary addition. Then we prove that all finite monogenic ternary semigroups with the same index...