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

TL;DR

This paper investigates the state complexity of non-unary self-verifying symmetric difference automata, showing that minimal deterministic automata can have exponentially more states than their nondeterministic counterparts.

Contribution

It extends the understanding of self-verifying symmetric difference automata from unary to non-unary cases, establishing bounds on state complexity and equivalence.

Findings

Existence of languages with exponential state complexity gap

Bound on the number of equivalent automata up to isomorphism

Extension of unary results to non-unary automata

Abstract

Previously, self-verifying symmetric difference automata were defined and a tight bound of 2^n-1-1 was shown for state complexity in the unary case. We now consider the non-unary case and show that, for every n at least 2, there is a regular language L_n accepted by a non-unary self-verifying symmetric difference nondeterministic automaton with n states, such that its equivalent minimal deterministic finite automaton has 2^n-1 states. Also, given any SV-XNFA with n states, it is possible, up to isomorphism, to find at most another |GL(n,Z_2)|-1 equivalent SV-XNFA.