We relate two measures of complexity of regular languages. The first is syntactic complexity, that is, the cardinality of the syntactic semigroup of the language. That semigroup is isomorphic to the semigroup of transformations of states induced by non-empty words in the minimal deterministic finite automaton accepting the language. If the language has n left quotients (its minimal automaton ha...

The notion of communication complexity was introduced by Yao in his seminal paper [Yao79]. In [BFS86], Babai Frankl and Simon developed a rich structure of communication complexity classes to understand the relationships between various models of communication complexity. This made it apparent that communication complexity was a self-contained mini-world within complexity theory. In this thesis...

In this paper we describe $${\mathcal {R}}$$ -unipotent semigroups being regular extensions of a left band by an $$\mathcal {R}$$ semigroup T as certain subsemigroups wreath product T. We obtain Szendrei’s result that each E-unitary is embeddable into semidirect group. Further, specialising the first author’s notion $$\lambda $$ -semidirect locally semigroup, provide answer to open question rai...

A poset is said to be ω-chain complete if every countable chain in it has a least upper bound. It is known that every partially ordered set has a natural ω-completion. In this paper we study the ω-completion of partially ordered semigroups, and the topological action of such a semigroup on its ω-completion. We show that, for partially ordered semigroups, ω-completion and quotient with respect t...

The generators of the Temperley-Lieb algebra generate a monoid with an appealing geometric representation. It has been much studied, notably by Louis Kau¤man. Borisavljevíc, Došen and Petríc gave a complete proof of its abstract presentation by generators and relations, and suggested the name ‘Kau¤man monoid’. We bring the theory of semigroups to the study of a certain …nite homomorphic image o...