Abstract
AbstractWe study the nondeterministic state complexity of basic regular operations on subregular language families. In particular, we focus on the classes of combinational, finitely generated left ideal, group, star, comet, two-sided comet, ordered, and power-separating languages, and consider the operations of intersection, union, concatenation, power, Kleene star, reversal, and complementation. We get the exact complexity in all cases, except for complementation of group languages where we only have an exponential lower bound. The complexity of all operations on combinational languages is given by a constant function, except for the k-th power where it is \(k+1\). For all considered operations, the known upper bounds for left ideals are met by finitely generated left ideal languages. The nondeterministic state complexity of the k-th power, star, and reversal on star languages is n. In all the remaining cases, the nondeterministic state complexity of all considered operations is the same as in the regular case, although sometimes we need to use a larger alphabet to describe the corresponding witnesses.
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