Regular ω-languages with an informative right congruence

Dana Angluin; Dana Fisman

doi:10.1016/j.ic.2020.104598

Regular ω-languages with an informative right congruence

Dana Angluin, Dana Fisman

Department of Computer Science

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

A regular language is almost fully characterized by its right congruence relation. The same does not hold for regular ω-languages. The right congruence of a regular ω-language may not be informative enough; many regular ω-languages have a trivial right congruence, and in general it is not always possible to define an ω-automaton recognizing a given language that is isomorphic to its right congruence. The weak regular ω-languages do have fully informative right congruences. That is, any weak regular ω-language can always be recognized by a deterministic Bu¨chi automaton that is isomorphic to its right congruence. Weak regular ω-languages reside in the lower levels of the expressiveness hierarchy of regular ω-languages. Are there more expressive sub-classes of regular ω-languages that have fully informative right congruences? Can we characterize the class of languages that have trivial right congruences? In this paper we try to place some additional pieces of this big puzzle.

Original language	English
Article number	104598
Journal	Information and Computation
Volume	278
DOIs	https://doi.org/10.1016/j.ic.2020.104598
State	Published - 1 Jun 2021

ASJC Scopus subject areas

Theoretical Computer Science
Information Systems
Computer Science Applications
Computational Theory and Mathematics

Access to Document

10.1016/j.ic.2020.104598

Cite this

@article{828dc0b1aa7f499e80caad95223deb5c,

title = "Regular ω-languages with an informative right congruence",

abstract = "A regular language is almost fully characterized by its right congruence relation. The same does not hold for regular ω-languages. The right congruence of a regular ω-language may not be informative enough; many regular ω-languages have a trivial right congruence, and in general it is not always possible to define an ω-automaton recognizing a given language that is isomorphic to its right congruence. The weak regular ω-languages do have fully informative right congruences. That is, any weak regular ω-language can always be recognized by a deterministic Bu¨chi automaton that is isomorphic to its right congruence. Weak regular ω-languages reside in the lower levels of the expressiveness hierarchy of regular ω-languages. Are there more expressive sub-classes of regular ω-languages that have fully informative right congruences? Can we characterize the class of languages that have trivial right congruences? In this paper we try to place some additional pieces of this big puzzle.",

author = "Dana Angluin and Dana Fisman",

note = "Funding Information: This is a revised and expanded version of a paper of the same title presented at GandALF 2018. In the earlier paper, the right side of Fig. 1 (p. 2) did not faithfully represent the results; it has been corrected. We thank the reviewers for their thoughtful comments. This research was supported by grant # 8758451 from the United States - Israel Binational Science Foundation (BSF), Jerusalem, Israel. Publisher Copyright: {\textcopyright} 2020 Elsevier Inc.",

year = "2021",

month = jun,

day = "1",

doi = "10.1016/j.ic.2020.104598",

language = "English",

volume = "278",

journal = "Information and Computation",

issn = "0890-5401",

publisher = "Elsevier Inc.",

}

TY - JOUR

T1 - Regular ω-languages with an informative right congruence

AU - Angluin, Dana

AU - Fisman, Dana

N1 - Funding Information: This is a revised and expanded version of a paper of the same title presented at GandALF 2018. In the earlier paper, the right side of Fig. 1 (p. 2) did not faithfully represent the results; it has been corrected. We thank the reviewers for their thoughtful comments. This research was supported by grant # 8758451 from the United States - Israel Binational Science Foundation (BSF), Jerusalem, Israel. Publisher Copyright: © 2020 Elsevier Inc.

PY - 2021/6/1

Y1 - 2021/6/1

N2 - A regular language is almost fully characterized by its right congruence relation. The same does not hold for regular ω-languages. The right congruence of a regular ω-language may not be informative enough; many regular ω-languages have a trivial right congruence, and in general it is not always possible to define an ω-automaton recognizing a given language that is isomorphic to its right congruence. The weak regular ω-languages do have fully informative right congruences. That is, any weak regular ω-language can always be recognized by a deterministic Bu¨chi automaton that is isomorphic to its right congruence. Weak regular ω-languages reside in the lower levels of the expressiveness hierarchy of regular ω-languages. Are there more expressive sub-classes of regular ω-languages that have fully informative right congruences? Can we characterize the class of languages that have trivial right congruences? In this paper we try to place some additional pieces of this big puzzle.

AB - A regular language is almost fully characterized by its right congruence relation. The same does not hold for regular ω-languages. The right congruence of a regular ω-language may not be informative enough; many regular ω-languages have a trivial right congruence, and in general it is not always possible to define an ω-automaton recognizing a given language that is isomorphic to its right congruence. The weak regular ω-languages do have fully informative right congruences. That is, any weak regular ω-language can always be recognized by a deterministic Bu¨chi automaton that is isomorphic to its right congruence. Weak regular ω-languages reside in the lower levels of the expressiveness hierarchy of regular ω-languages. Are there more expressive sub-classes of regular ω-languages that have fully informative right congruences? Can we characterize the class of languages that have trivial right congruences? In this paper we try to place some additional pieces of this big puzzle.

UR - http://www.scopus.com/inward/record.url?scp=85086448817&partnerID=8YFLogxK

U2 - 10.1016/j.ic.2020.104598

DO - 10.1016/j.ic.2020.104598

M3 - Article

AN - SCOPUS:85086448817

SN - 0890-5401

VL - 278

JO - Information and Computation

JF - Information and Computation

M1 - 104598

ER -

Regular ω-languages with an informative right congruence

Abstract

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this