Abstract
To a given language L, we associate the sets ins(L) (resp. del(L)) consisting of words with the following property: their insertion into (deletion from) any word of L yields words which also belong to L. Properties of these sets and of languages which are insertion (deletion) closed are obtained. Of special interest is the case when the language is ins-closed (del-closed) and finitely generated. Then the minimal set of generators turns out to be a maximal prefix and suffix code, which is regular if L is regular. In addition, we study the insertion-base of a language and languages which have the property that both they and their complements are ins-closed.
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