Some more on omega-finite automata and omega-regular languages. Part I: The main definitions and properties

Boris Melnikov, Aleksandra Melnikova

Abstract


The finite and infinite iterations of finite and infinite languages arise in various problems of the formal languages theory.
For instance, we can mention their application for the description of subclasses of the context-free languages class with the decidable equivalence problem.
For infinite iterations of finite languages, we consider in this paper so-called strongly connected omega-automata and corresponding omega-regular languages.
For them, many statements are fulfilled that are not satisfied in the more general case, i.e. when we use arbitrary omega-finite automata and corresponding omega-regular languages; the omega-iterations of languages include in the class of strongly connected omega-regular languages.
The main of such properties and statements are non-existence of an omega-automaton for which there is no equivalent deterministic, and the possibility of checking the equivalence of two given omega-automata; in the general case (i.e., when we consider arbitrary omega-automata), both of these properties are not satisfied.
We also describe transferring the usual procedure of determinization to the case of omega-automata and show the correctness of this procedure in the cases we are considering.
We consider some examples, and in the second part of the paper, we shall consider the transfer of a well-known example (so called Waterloo automaton) to the case of omega-automata and omega-languages.


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References


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