Algebraic and Combinatorial Tools for State Complexity : Application to the Star-Xor Problem

Abstract

We investigate the state complexity of the star of symmetrical differences using modifiers and monsters. A monster is an automaton in which every function from states to states is represented by at least one letter. A modifier is a set of functions allowing one to transform a set of automata into one automaton. These recent theoretical concepts allow one to find easily the desired state complexity. We then exhibit a witness with a constant size alphabet.