On a subclass of the regular language class (“strongly connected” languages): definitions and corresponding canonical automata

Boris Melnikov

Abstract


In our previous publications, we considered a simplified version of the definition of omega-automata that define omega-languages compared to the classics. However, despite this “simplification”, such a definition makes it possible to specify the subclasses of the class of omega-languages that we need in a lot of problems, to describe the corresponding algorithms for equivalent transformations of the omegaautomata we have defined, etc. At the same time, we have already considered a group of questions related to omega automata and the corresponding omega computations, but which, with some reformulation, can also be attributed to ordinary nondeterministic finite automata. We have defined iterating and strongly connected omega automata; however, based on the definitions and properties of such automata discussed in previous papers, we can conclude that almost the same concepts can be applied to ordinary NFAs. In this regard, in this paper we define strongly connected automata as a subset of ordinary NFAs. Based on this concept, we define strongly connected languages, and then show their relation to the invariants available in the class of regular languages: canonical, basis, and universal finite automata. In particular, we show that for a strongly connected language and its mirror image, all 4 variants of the strong connectivity condition of the corresponding canonical automata are possible. In this paper, as well as in the proposed continuations, we shall consider subclasses of strongly connected languages, present algorithms for equivalent transformation of corresponding strongly connected automata, describe some special subclasses of the class of strongly connected languages and some properties of these subclasses. They will give the possibility to describe algorithms of equivalent transformations for the above-mentioned variant of omega-automata.

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References


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