research-article

Adding Successor: A Transfer Theorem for Separation and Covering

Authors:

Marc ZeitounAuthors Info & Claims

ACM Transactions on Computational Logic (TOCL), Volume 21, Issue 2

Article No.: 9, Pages 1 - 45

https://doi.org/10.1145/3356339

Published: 17 November 2019 Publication History

Abstract

Given a class C of word languages, the C-separation problem asks for an algorithm that, given as input two regular languages, decides whether there exists a third language in C containing the first language, while being disjoint from the second. Separation is usually investigated as a means to obtain a deep understanding of the class C.

In this article, we are mainly interested in classes defined by logical formalisms. Such classes are often built on top of each other: given some logic, one builds a stronger one by adding new predicates to its signature. A natural construction is to enrich a logic with the successor relation. In this article, we present a transfer result applying to this construction: We show that for suitable logically defined classes, separation for the logic enriched with the successor relation reduces to separation for the original logic. Our theorem also applies to a problem that is stronger than separation: covering. Moreover, we actually present two reductions: one for languages of finite words and the other for languages of infinite words.

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Cited By

Volaříková J(2024)The omega-reducibility of pseudovarieties of ordered monoids representing low levels of concatenation hierarchiesInternational Journal of Algebra and Computation10.1142/S021819672450002434:01(87-135)Online publication date: 7-Mar-2024
https://doi.org/10.1142/S0218196724500024
Artale AJung JMazzullo AOzaki AWolter F(2023)Living without Beth and Craig: Definitions and Interpolants in Description and Modal Logics with Nominals and Role InclusionsACM Transactions on Computational Logic10.1145/359730124:4(1-51)Online publication date: 10-Oct-2023
https://dl.acm.org/doi/10.1145/3597301
Place T(2022)The amazing mixed polynomial closure and its applications to two-variable first-order logicProceedings of the 37th Annual ACM/IEEE Symposium on Logic in Computer Science10.1145/3531130.3532410(1-14)Online publication date: 2-Aug-2022
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Index Terms

Adding Successor: A Transfer Theorem for Separation and Covering
1. Theory of computation
  1. Formal languages and automata theory
    1. Regular languages
  2. Logic

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Published In

cover image ACM Transactions on Computational Logic

ACM Transactions on Computational Logic Volume 21, Issue 2

April 2020

316 pages

ISSN:1529-3785

EISSN:1557-945X

DOI:10.1145/3371152

Editor:
Orna Kupferman
School of Computer Science and Engineering, Hebrew University, Israel

Issue’s Table of Contents

Copyright © 2019 ACM.

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 17 November 2019

Accepted: 01 August 2019

Revised: 01 March 2019

Received: 01 December 2017

Published in TOCL Volume 21, Issue 2

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Cited By

Volaříková J(2024)The omega-reducibility of pseudovarieties of ordered monoids representing low levels of concatenation hierarchiesInternational Journal of Algebra and Computation10.1142/S021819672450002434:01(87-135)Online publication date: 7-Mar-2024
https://doi.org/10.1142/S0218196724500024
Artale AJung JMazzullo AOzaki AWolter F(2023)Living without Beth and Craig: Definitions and Interpolants in Description and Modal Logics with Nominals and Role InclusionsACM Transactions on Computational Logic10.1145/359730124:4(1-51)Online publication date: 10-Oct-2023
https://dl.acm.org/doi/10.1145/3597301
Place T(2022)The amazing mixed polynomial closure and its applications to two-variable first-order logicProceedings of the 37th Annual ACM/IEEE Symposium on Logic in Computer Science10.1145/3531130.3532410(1-14)Online publication date: 2-Aug-2022
https://dl.acm.org/doi/10.1145/3531130.3532410
Steinberg B(2021)Pointlike Sets and Separation: A Personal PerspectiveDevelopments in Language Theory10.1007/978-3-030-81508-0_3(27-40)Online publication date: 6-Aug-2021
https://doi.org/10.1007/978-3-030-81508-0_3

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