Polynomial-time Equational Theory for Lattices with Unary Operators

The equational theory of the class of lattices with a pair of unary residuated operations is shown to be decidable in O ( n 5 ) time. The same complexity holds in the bounded case. The equational theory of the class of lattices, as well as the class of bounded lattices, with a unary operator is show...

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Bibliographic Details
Published in:Order (Dordrecht) Vol. 42; no. 3; pp. 645 - 662
Main Author: Van Alten, C.J.
Format: Journal Article
Language:English
Published: Dordrecht Springer Netherlands 01.12.2025
Springer Nature B.V
Subjects:
Algebra
Algorithms
Calculus
Discrete Mathematics
Dynamic programming
Lattices
Mathematics
Mathematics and Statistics
Order
Ordered Algebraic Structures
Polynomials
Lattice with operator
Polynomial-time algorithm
Unary residuated lattice
Equational theory
ISSN:0167-8094, 1572-9273
Online Access:Get full text
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Summary:The equational theory of the class of lattices with a pair of unary residuated operations is shown to be decidable in O ( n 5 ) time. The same complexity holds in the bounded case. The equational theory of the class of lattices, as well as the class of bounded lattices, with a unary operator is shown to be decidable in O ( n 3 ) time. Explicit algorithms are given for deciding the above equational theories. These algorithms use a dynamic programming approach and are based on a sequent calculus that extends Whitman’s sequent calculus for lattices.
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ISSN:0167-8094
1572-9273
DOI:10.1007/s11083-025-09701-4