EFFICIENT CONSTRUCTIONS OF TEST SETS FOR REGULAR AND CONTEXT-FREE LANGUAGES

We present a simple construction of linear size test sets for regular languages and of single exponential test sets for context free languages. In the case of regular sets the size of our test set is exactly the number of transitions of the automaton. This improves the best known upper bounds: exponential for regular and doubly exponential for context-free languages. We give also an O(n log n) time algorithm for the morphism equivalence and an O(n3log n) time algorithm to best the gsm equivalence on a regular language. An O(n2log n) time algorithm is given to test the equivalence of two deterministic gsm's as well as that of two deterministic finite transducers.