State complexity of unary SV-XNFA with different acceptance conditions

Unary self-verifying symmetric difference automata were introduced in [1], with an upper bound of \(O(2^{n})\) and lower bound of \(2^{n-1}-1\) for state complexity. Implicit in the interpretation of self-verifying acceptance for the symmetric difference case was the assumption that no state could be both an accept state and a reject state. We present another interpretation of acceptance more aligned to the equivalence of symmetric difference automata to weighted automata over GF(2), where states that both accept and reject are allowed, and we give a tight bound of \(2^{n-1}-1\) for state complexity for both interpretations of acceptance.