Ambiguity and structural ambiguity of symmetric difference NFAs

Okhotin showed an exponential trade-off in the conversion from nondeterministic unary automata to unambiguous nondeterministic unary automata. We show that the trade-off in the case of unary symmetric difference automata to finitely (structurally) ambiguous unary symmetric difference automata is linear with constant 1 in the number of states. In particular, for every n-state unary nondeterministic symmetric difference automaton, there is an equivalent finitely (structurally) ambiguous n-state unary symmetric difference nondeterministic automaton. We also consider the complexity of deciding unambiguity for k-deterministic finite automata and investigate the interplay between ambiguity and structural ambiguity.