Operational state complexity of unary NFAs with finite nondeterminism

We study the state complexity of language operations for unary NFAs with limited nondeterminism. We consider the Boolean operations, concatenation, and Kleene star. We give upper bounds for the state complexity of these language operations and lower bounds that are fairly close to the upper bounds. Our constructions rely on the fact that minimal unary NFAs with limited nondeterminism can be found in Chrobak normal form for most measures of nondeterminism. The measures of nondeterminism which are considered here with the above property are tree width, advice, and trace.