Languages of partial Words - how to obtain them and what properties they have, Formal Grammars

Partial words were introduced by Berstel and Boasson in 1999. Since then various of their combinatorial properties have been studied, the foremost being periodicity. Lately Blanchet-Sadri has made a first step in also investigating languages of partial words by introducing the concept of pcodes. With a slightly different approach we define new ways to obtain such languages by puncturing conventional ones. Then we present some first results on properties like the finiteness of their root or the property of being a code for these newly defined punctured languages.