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Computer Science > Formal Languages and Automata Theory

arXiv:1809.03108v1 (cs)
[Submitted on 10 Sep 2018]

Title:Regular omega-Languages with an Informative Right Congruence

Authors:Dana Angluin (Yale University), Dana Fisman (Ben-Gurion University)
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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 Büchi 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.
Comments: In Proceedings GandALF 2018, arXiv:1809.02416
Subjects: Formal Languages and Automata Theory (cs.FL); Machine Learning (cs.LG)
Cite as: arXiv:1809.03108 [cs.FL]
  (or arXiv:1809.03108v1 [cs.FL] for this version)
  https://doi.org/10.48550/arXiv.1809.03108
Journal reference: EPTCS 277, 2018, pp. 265-279
Related DOI: https://doi.org/10.4204/EPTCS.277.19

Submission history

From: EPTCS [view email] [via EPTCS proxy]
[v1] Mon, 10 Sep 2018 02:35:18 UTC (35 KB)
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