Ambiguity of Unary Symmetric Difference NFAs

Okhotin [9] showed an exponential trade-off in the conversion from nondeterministic unary finite automata to unambiguous nondeterministic unary finite automata. In this paper, we consider the trade-off in the case of unary symmetric difference finite automata to finitely ambiguous unary symmetric difference finite automata. Surprisingly, the trade-off is linear in the number of states of the finite automaton. In particular, for every n-state unary nondeterministic symmetric difference finite automaton, there is an equivalent finitely ambiguous n-state unary symmetric difference nondeterministic finite automaton. We also note other relevant ambiguity issues in the unary case, such as the ambiguity of k-deterministic finite automata.