On Nonpermutational Transformation Semigroups with an Application to Syntactic Complexity

Abstract

We give an upper bound of n((n-1)!-(n-3)!) for the possible largest size of a subsemigroup of the full transformational semigroup over n elements consisting only of nonpermutational transformations. As an application we gain the same upper bound for the syntactic complexity of (generalized) definite languages as well.