The Average State Complexity of the Star of a Finite Set of Words Is Linear

We prove that, for the uniform distribution over all sets X of m (that is a fixed integer) non-empty words whose sum of lengths is n, DX , one of the usual deterministic automata recognizing X , has on average O(n) states and that the average state complexity of X is (n). We also show that the average time complexity of the computation of the automaton DX is O(n log n), when the alphabet is of size at least three.

• Type: Conference
• Year: 2008
• Where: DLT
• Authors: Frédérique Bassino, Laura Giambruno, Cyril Nicaud
• Keywords: Average State Complexity, Average Time Complexity, DLT 2008, Theoretical Computer Science, Usual Deterministic Automata