State Complexity of Catenation Combined with a Boolean Operation: A Unified Approach

Pascal Caron (1, 2) , Jean-Gabriel Luque (1, 2) , Ludovic Mignot (3, 2) , Bruno Patrou (1, 2)

1 CA - LITIS - Equipe Combinatoire et algorithmes
2 UNIROUEN - Université de Rouen Normandie
3 LITIS - Laboratoire d'Informatique, de Traitement de l'Information et des Systèmes

We study the state complexity of catenation combined with symmetric difference. First, an upper bound is computed using some combinatoric tools. Then, this bound is shown to be tight by giving a witness for it. Moreover, we relate this work with the study of state complexity for two other combinations: catenation with union and catenation with intersection. We extract a unified approach which allows to obtain the state complexity of any combination involving catenation and a binary boolean operation.

Keywords: State complexity; boolean operations; catenation; Brzozowski automata

Domains: Computer Science [cs]

Pascal Caron, Jean-Gabriel Luque, Ludovic Mignot, Bruno Patrou. State Complexity of Catenation Combined with a Boolean Operation: A Unified Approach. International Journal of Foundations of Computer Science, 2016, 27 (06), pp.675-703. ⟨10.1142/S0129054116500234⟩. ⟨hal-02088118⟩