Open Problems on Partial Words

Combinatorics on words, or sequences or strings of symbols over a finite alphabet, is a rather new field although the first papers were published at the beginning of the 20th century [120, 121]. The interest in the study of combinatorics on words has been increasing since it finds applications in various research areas of mathematics, computer science, and biology where the data can be easily represented as words over some alphabet. Such areas may be concerned with algorithms on strings [38, 48, 50, 51, 52, 69, 72, 84, 102, 118], semigroups, automata and languages [2, 45, 55, 75, 82, 92, 93], molecular genetics [78], or codes [5, 73, 79].

Motivated by molecular biology of nucleic acids, Berstel and Boasson introduced in 1999 the notion of partial words which are sequences that may contain a number of “do not know” symbols or “holes” [4]. DNA molecules are the carriers of the genetic information in almost all organisms.