SAT-Based Techniques for Lexicographically Smallest Finite Models
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21730%2F24%3A00375284" target="_blank" >RIV/68407700:21730/24:00375284 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1609/aaai.v38i8.28643" target="_blank" >https://doi.org/10.1609/aaai.v38i8.28643</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1609/aaai.v38i8.28643" target="_blank" >10.1609/aaai.v38i8.28643</a>
Alternative languages
Result language
angličtina
Original language name
SAT-Based Techniques for Lexicographically Smallest Finite Models
Original language description
This paper proposes SAT-based techniques to calculate a specific normal form of a given finite mathematical structure (model). The normal form is obtained by permuting the domain elements so that the representation of the structure is lexicographically smallest possible. Such a normal form is of interest to mathematicians as it enables easy cataloging of algebraic structures. In particular, two structures are isomorphic precisely when their normal forms are the same. This form is also natural to inspect as mathematicians have been using it routinely for many decades. We develop a novel approach where a SAT solver is used in a black-box fashion to compute the smallest representative. The approach constructs the representative gradually and searches the space of possible isomorphisms, requiring a small number of variables. However, the approach may lead to a large number of SAT calls and therefore we devise propagation techniques to reduce this number. The paper focuses on finite structures with a single binary operation (encompassing groups, semigroups, etc.). However, the approach is generalizable to arbitrary finite structures. We provide an implementation of the proposed algorithm and evaluate it on a variety of algebraic structures.
Czech name
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Czech description
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Classification
Type
D - Article in proceedings
CEP classification
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OECD FORD branch
10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)
Result continuities
Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Article name in the collection
Proceedings of the 38th AAAI Conference on Artificial Intelligence
ISBN
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ISSN
2159-5399
e-ISSN
2374-3468
Number of pages
9
Pages from-to
8048-8056
Publisher name
AAAI Press
Place of publication
Menlo Park
Event location
Vancouver
Event date
Feb 20, 2024
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
001239938200016