Automated reasoning and exhaustive search: Quasigroup existence problems
type: Item
instance of: scholarly article
title: Automated reasoning and exhaustive search: Quasigroup existence problems
zbMATH Open document ID: 0827.20083
DOI: 10.1016/0898-1221(94)00219-B
author: V. Pereyra
publication date: 1995-12-03T00:00:00Z
review text: The authors investigate the existence of some finite quasigroups using three different automated reasoning programs: DDPP, FINDER and MGTP. Their attention is concentrated on some \((i,j,k)\)-conjugate orthogonal idempotent Latin squares of order \(v\) (COILS(\(v\))) and quasigroups satisfying one of the identities: \(ab.ba=a\), \(ab.ba=b\), \((ba.b)b=a\), \(ab.b=a.ab\), \(a.ba=ba.b\), where the order is some \(v \geq 8\). The existence or nonexistence is proved by experimental evidence. The computations of such hard problems are very complicated. The programs DDPP, FINDER and MGTP are described, and in several cases the authors give their search times for comparison.
Mathematics Subject Classification ID: 20N05
Mathematics Subject Classification ID: 20-04
Mathematics Subject Classification ID: 05B15
Mathematics Subject Classification ID: 68T15
Mathematics Subject Classification ID: 68W30
zbMATH DE Number: 718814
zbMATH Keywords: finite quasigroups
zbMATH Keywords: automated reasoning programs
zbMATH Keywords: orthogonal idempotent Latin squares
zbMATH Keywords: identities
reviewed by: Elena Broží ková
describes a project that uses: FINDER
MaRDI profile type: Publication
cites work: Q4026145
cites work: Quasigroup Identities and Mendelsohn Designs
cites work: Quasigroups and tactical systems
cites work: Q5587083
cites work: Algorithms for finding matrix models of propositional calculi
cites work: Constraint satisfaction from a deductive viewpoint
cites work: Q4934645
cites work: Linear programming in some Ramsey problems
full work available at URL: 0898-1221(94)00219-b
OpenAlex ID: W2082167089
published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 718814