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An Efficient Nominal Unification Algorithm

Nominal Unification is an extension of first-order unification where terms can contain binders and unification is performed modulo α equivalence. Here we prove that the existence of nominal unifiers can be decided in quadratic time. First, we linearly-reduce nominal unification problems to a sequence of freshness and equalities between atoms, modulo a permutation, using ideas as Paterson and Wegman for first-order unification. Second, we prove that solvability of these reduced problems may be checked in quadràtic time. Finally, we point out how using ideas of Brown and Tarjan for unbalanced merging, we could solve these reduced problems more efficiently

Dagstuhl Publishing

Author: Levy, Jordi
Villaret i Ausellé, Mateu
Abstract: Nominal Unification is an extension of first-order unification where terms can contain binders and unification is performed modulo α equivalence. Here we prove that the existence of nominal unifiers can be decided in quadratic time. First, we linearly-reduce nominal unification problems to a sequence of freshness and equalities between atoms, modulo a permutation, using ideas as Paterson and Wegman for first-order unification. Second, we prove that solvability of these reduced problems may be checked in quadràtic time. Finally, we point out how using ideas of Brown and Tarjan for unbalanced merging, we could solve these reduced problems more efficiently
Document access: http://hdl.handle.net/2072/294833
Language: eng
Publisher: Dagstuhl Publishing
Rights: Attribution-NonCommercial-NoDerivs 3.0 Spain
Rights URI: http://creativecommons.org/licenses/by-nc-nd/3.0/es/
Subject: Algorismes computacionals
Computer algorithms
Lògica matemàtica
Logic, Symbolic and mathematical
Complexitat computacional
Computational complexity
Title: An Efficient Nominal Unification Algorithm
Type: info:eu-repo/semantics/article
Repository: Recercat

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