State complexity of multiple catenation

Pascal Caron (1, 2) , Jean-Gabriel Luque (1, 2) , Bruno Patrou (1, 2)

1 CA - LITIS - Equipe Combinatoire et algorithmes
2 UNIROUEN - Université de Rouen Normandie

We improve some results relative to the state complexity of the multiple catenation described by Gao and Yu. In particular we nearly divide by 2 the size of the alphabet needed for witnesses. We also give some refinements to the algebraic expression of the state complexity, which is especially complex with this operation. We obtain these results by using peculiar DFAs defined by Brzozowski.

Domaines: Informatique [cs]

Pascal Caron, Jean-Gabriel Luque, Bruno Patrou. State complexity of multiple catenation. 2019. ⟨hal-02088131⟩