In mathematics, the bicyclic semigroup is an algebraic object important for the structure theory of semigroups. Although it is in fact a monoid, it is...

finite-state machine (FSM). The bicyclic semigroup is in fact a monoid, which can be described as the free semigroup on two generators p and q, under...

meant by a regular band. The bicyclic semigroup is regular. Any full transformation semigroup is regular. A Rees matrix semigroup is regular. The homomorphic...

semigroup S. Partial bijections on a set X form an inverse semigroup under composition. Every group is an inverse semigroup. The bicyclic semigroup is...

a finite set of generators is compact. The bicyclic monoid is not compact. The class of compact semigroups is closed under taking subsemigroups and finite...

presentation of a monoid (or a presentation of a semigroup) is a description of a monoid (or a semigroup) in terms of a set Σ of generators and a set of...

matrix semigroup over the bicyclic semigroup, and the four-spiral semigroup Sp4 is isomorphic to S. By definition itself, the four-spiral semigroup is an...

. The syntactic monoid of the Dyck language is isomorphic to the bicyclic semigroup by virtue of the properties of Cl ⁡ ( [ ) {\displaystyle \operatorname...

classes of semigroups, notably completely simple semigroups (Campbell et al. 2002) and group-embeddable semigroups (Cain et al. 2006). Bicyclic monoid Finitely...

mathematics, a semigroup is a nonempty set together with an associative binary operation. A special class of semigroups is a class of semigroups satisfying...