Abstract
Nondeterministic finite Rabin-Scott's automata without initial and final states (2 $\omega$-FA) are considered. In this paper they are used to define so called sets of obstruction used also in various alge-braic systems and to consider similar problems for the formal languages theory. Thus we define sets of obstructions of languages(or, rather, 2$\omega$-languages) of such automata. We obtain that each 2$\omega$-language defined by 2 $\omega$-FA has the set of obstruction being a regular language. And vice versa for each regular language L(containing no proper subword of its another word) there exists a 2$\omega$ -FA having L as the set of obstructions.