Cover Complexity of Finite Languages
We consider the notion of cover complexity of finite languages on three different levels of abstraction. For arbitrary cover complexity measures, we give a characterisation of the situations in which they collapse to a bounded complexity measure. Moreover, we show for a restricted class of context-free grammars that its grammatical cover complexity measure w.r.t. a finite language L is unbounded and that the cover complexity of L can be computed from the exact complexities of a finite number of covers \(L' \supseteq L\). We also investigate upper and lower bounds on the grammatical cover complexity of the language operations intersection, union, and concatenation on finite languages for several different types of context-free grammars.
The authors would like to thank Markus Holzer and the anonymous reviewers for several useful comments and suggestions concerning the results in this paper.