Languages and monoids with disjunctive identity (Q1911748)

This paper considers syntactic monoids of some classes of languages related to the operations of insertion and deletion. These classes of languages are: insertion-closed; deletion-closed and dipolar-closed. It is shown that syntactic monoids of insertion-closed and dipolar-closed languages are groups. If the languages are insertion-closed and congruence-simple, then their syntactic monoids are the monoids with disjunctive identity. Properties of insertion-closed or deletion-closed languages have been considered by \textit{M. Ito} and the author [Insertion and deletion closure of languages (to appear in Theor. Comput. Sci.)]. One of the sections gives properties of dipolar-closed languages.