Descriptional Complexity of Non-Unary Self-Verifying Symmetric Difference Automata

Abstract

Unary self-verifying symmetric difference automata have a known tight bound of [Formula: see text] for their state complexity. We now consider the non-unary case and show that, for every [Formula: see text], there is a regular language [Formula: see text] accepted by a non-unary self-verifying symmetric difference nondeterministic automaton with [Formula: see text] states, such that its equivalent minimal deterministic finite automaton has [Formula: see text] states. Furthermore, given any SV-XNFA with [Formula: see text] states, it is possible, up to isomorphism, to find at most another [Formula: see text] equivalent SV-XNFA. Finally, we show that for a certain set of non-unary SV-XNFA, [Formula: see text] is a tight bound on the state complexity.