Regular omega-Languages with an Informative Right Congruence
release_n4cdewi3cfhjfokls6ktl7dqxy
by
Dana Angluin
2018
Abstract
A regular language is almost fully characterized by its right congruence
relation. Indeed, a regular language can always be recognized by a DFA
isomorphic to the automaton corresponding to its right congruence, henceforth
the Rightcon automaton. The same does not hold for regular omega-languages. The
right congruence of a regular omega-language is not informative enough; many
regular omega-languages have a trivial right congruence, and in general it is
not always possible to define an omega-automaton recognizing a given language
that is isomorphic to the rightcon automaton.
The class of weak regular omega-languages does have an informative right
congruence. That is, any weak regular omega-language can always be recognized
by a deterministic B\"uchi automaton that is isomorphic to the rightcon
automaton. Weak regular omega-languages reside in the lower levels of the
expressiveness hierarchy of regular omega-languages. Are there more expressive
sub-classes of regular omega languages that have an informative right
congruence? Can we fully characterize the class of languages with a trivial
right congruence? In this paper we try to place some additional pieces of this
big puzzle.
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1809.03108v1
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