research-article

Idempotent Anti-unification

Authors:

Temur KutsiaAuthors Info & Claims

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

Article No.: 10, Pages 1 - 32

https://doi.org/10.1145/3359060

Published: 02 November 2019 Publication History

Abstract

In this article, we address two problems related to idempotent anti-unification. First, we show that there exists an anti-unification problem with a single idempotent symbol that has an infinite minimal complete set of generalizations. It means that anti-unification with a single idempotent symbol has infinitary or nullary generalization type, similar to anti-unification with two idempotent symbols, shown earlier by Loïc Pottier. Next, we develop an algorithm that takes an arbitrary idempotent anti-unification problem and computes a representation of its solution set in the form of a regular tree grammar. The algorithm does not depend on the number of idempotent function symbols in the input terms. The language generated by the grammar is the minimal complete set of generalizations of the given anti-unification problem, which implies that idempotent anti-unification is infinitary.

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Cited By

Cerna DBuran M(2024)One or Nothing: Anti-unification over the Simply-Typed Lambda CalculusACM Transactions on Computational Logic10.1145/365479825:3(1-12)Online publication date: 28-Mar-2024
https://dl.acm.org/doi/10.1145/3654798
Ayala-Rincón MCerna DBarragán AKutsia T(2024)Equational Anti-unification over Absorption TheoriesAutomated Reasoning10.1007/978-3-031-63501-4_17(317-337)Online publication date: 2-Jul-2024
https://doi.org/10.1007/978-3-031-63501-4_17
Cerna DKutsia TElkind E(2023)Anti-unification and generalizationProceedings of the Thirty-Second International Joint Conference on Artificial Intelligence10.24963/ijcai.2023/736(6563-6573)Online publication date: 19-Aug-2023
https://dl.acm.org/doi/10.24963/ijcai.2023/736
Show More Cited By

Index Terms

Idempotent Anti-unification
1. Theory of computation
  1. Formal languages and automata theory

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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

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Copyright © 2019 ACM.

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Publication History

Published: 02 November 2019

Accepted: 01 August 2019

Revised: 01 June 2019

Received: 01 January 2019

Published in TOCL Volume 21, Issue 2

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Cited By

Cerna DBuran M(2024)One or Nothing: Anti-unification over the Simply-Typed Lambda CalculusACM Transactions on Computational Logic10.1145/365479825:3(1-12)Online publication date: 28-Mar-2024
https://dl.acm.org/doi/10.1145/3654798
Ayala-Rincón MCerna DBarragán AKutsia T(2024)Equational Anti-unification over Absorption TheoriesAutomated Reasoning10.1007/978-3-031-63501-4_17(317-337)Online publication date: 2-Jul-2024
https://doi.org/10.1007/978-3-031-63501-4_17
Cerna DKutsia TElkind E(2023)Anti-unification and generalizationProceedings of the Thirty-Second International Joint Conference on Artificial Intelligence10.24963/ijcai.2023/736(6563-6573)Online publication date: 19-Aug-2023
https://dl.acm.org/doi/10.24963/ijcai.2023/736
Alpuente MBallis DEscobar SSapiña J(2022)Variant-Based Equational Anti-unificationLogic-Based Program Synthesis and Transformation10.1007/978-3-031-16767-6_3(44-60)Online publication date: 11-Sep-2022
https://doi.org/10.1007/978-3-031-16767-6_3
Cerna D(2020)Anti-unification and the theory of semiringsTheoretical Computer Science10.1016/j.tcs.2020.10.020848(133-139)Online publication date: Dec-2020
https://doi.org/10.1016/j.tcs.2020.10.020

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