Journal of the ACM (JACM)
String Matching Algorithms and Automata
Proceedings of the Colloquium in Honor of Arto Salomaa on Results and Trends in Theoretical Computer Science
Closures in Formal Languages and Kuratowski's Theorem
DLT '09 Proceedings of the 13th International Conference on Developments in Language Theory
On inverse operations and their descriptional complexity
DCFS'12 Proceedings of the 14th international conference on Descriptional Complexity of Formal Systems
Automatic theorem-proving in combinatorics on words
CIAA'12 Proceedings of the 17th international conference on Implementation and Application of Automata
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A language L is closed if L=L^@?. We consider an operation on closed languages, L^-^@?, that is an inverse to Kleene closure. It is known that if L is closed and regular, then L^-^@? is also regular. We show that the analogous result fails to hold for the context-free languages. Along the way we find a new relationship between the unbordered words and the prime palstars of Knuth, Morris, and Pratt. We use this relationship to enumerate the prime palstars, and we prove that neither the language of all unbordered words nor the language of all prime palstars is context-free.