Title:	Nominal anti-unification with atom-variables
Authors:	Schmidt-Schauß, Manfred Nantes Sobrinho, Daniele
metadata.dc.identifier.orcid:	https://orcid.org/0000-0001-8809-7385 https://orcid.org/0000-0002-1959-8730
metadata.dc.contributor.affiliation:	Goethe Universität, Frankfurt am Main Imperial College London, Department of Computing University of Brasília, Department of Mathematics
Assunto::	Anti-unificação Algoritmos nominais
Issue Date:	2022
Publisher:	Schloss Dagstuhl – Leibniz-Zentrum f¨ur Informatik
Citation:	SCHMIDT-SCHAUß, Manfred; NANTES-SOBRINHO, Daniele. Nominal anti-unification with atom-variables. In: INTERNATIONAL CONFERENCE ON FORMAL STRUCTURES FOR COMPUTATION AND DEDUCTION (FSCD 2022), 7th, v. 228, 2022. Dagstuhl, Germany: Leibniz International Proceedings in Informatics (LIPIcs), 2022, p. 1-22. DOI: 10.4230/LIPIcs.FSCD.2022.7. Disponível em: https://drops.dagstuhl.de/opus/volltexte/2022/16288/pdf/LIPIcs-FSCD-2022-7.pdf. Acesso em: 09 jul. 2023.
Abstract:	Anti-unification is the task of generalizing a set of expressions in the most specific way. It was extended to the nominal framework by Baumgarter, Kutsia, Levy and Villaret, who defined an algorithm solving the nominal anti-unification problem, which runs in polynomial time. Unfortunately, when an infinite set of atoms are allowed in generalizations, a minimal complete set of solutions in nominal anti-unification does not exist, in general. In this paper, we present a more general approach to nominal anti-unification that uses atom-variables instead of explicit atoms, and two variants of freshness constraints: NLA-constraints (with atom-variables), and Eqr-constraints based on Equivalence relations on atom-variables. The idea of atom-variables is that different atom-variables may be instantiated with identical or different atoms. Albeit simple, this freedom in the formulation increases its application potential: we provide an algorithm that is finitary for the NLA-freshness constraints, and for Eqr-freshness constraints it computes a unique least general generalization. There is a price to pay in the general case: checking freshness constraints and other related logical questions will require exponential time. The setting of Baumgartner et al. is improved by the atom-only case, which runs in polynomial time and computes a unique least general generalization
metadata.dc.description.unidade:	Instituto de Ciências Exatas (IE) Departamento de Matemática (IE MAT)
Licença::	Creative Commons Attribution 4.0 license (CC BY 4.0)
DOI:	10.4230/LIPIcs.FSCD.2022.7
Appears in Collections:	Trabalhos apresentados em evento

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