Complete Symmetry Breaking for Finite Models

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21730%2F25%3A00385117" target="_blank" >RIV/68407700:21730/25:00385117 - isvavai.cz</a>

Result on the web

<a href="https://doi.org/10.1609/aaai.v39i11.33217" target="_blank" >https://doi.org/10.1609/aaai.v39i11.33217</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1609/aaai.v39i11.33217" target="_blank" >10.1609/aaai.v39i11.33217</a>

Result language

angličtina

Original language name

Complete Symmetry Breaking for Finite Models

Original language description

This paper introduces a SAT-based technique that calculates a compact and complete symmetry-break for finite model finding, with the focus on structures with a single binary operation (magmas). Classes of algebraic structures are typically described as first-order logic formulas and the concrete algebras are models of these formulas. Such models include an enormous number of isomorphic, i.e. symmetric, algebras. A complete symmetry-break is a formula that has as models, exactly one canonical representative from each equivalence class of algebras. Thus, we enable answering questions about properties of the models so that computation and search are restricted to the set of canonical representations. For instance, we can answer the question: How many non-isomorphic semigroups are there of size n? Such questions can be answered by counting the satisfying assignments of a SAT formula, which already filters out non-isomorphic models. The introduced technique enables us calculating numbers of algebraic structures not present in the literature and going beyond the possibilities of pure enumeration approachesThis paper introduces a SAT-based technique that calculates a compact and complete symmetry-break for finite model finding, with the focus on structures with a single binary operation (magmas). Classes of algebraic structures are typically described as first-order logic formulas and the concrete algebras are models of these formulas. Such models include an enormous number of isomorphic, i.e. symmetric, algebras. A complete symmetry-break is a formula that has as models, exactly one canonical representative from each equivalence class of algebras. Thus, we enable answering questions about properties of the models so that computation and search are restricted to the set of canonical representations. For instance, we can answer the question: How many non-isomorphic semigroups are there of size n? Such questions can be answered by counting the satisfying assignments of a SAT formula, which already filters out non-isomorphic models. The introduced technique enables us calculating numbers of algebraic structures not present in the literature and going beyond the possibilities of pure enumeration approaches

Czech name

—

Czech description

—

Type

D - Article in proceedings

CEP classification

—

OECD FORD branch

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

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)

Publication year

2025

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Article name in the collection

Proceedings of the 39th AAAI Conference on Artificial Intelligence

ISBN

978-1-57735-897-8

ISSN

2159-5399

e-ISSN

2374-3468

Number of pages

9

Pages from-to

11194-11202

Publisher name

AAAI Press

Place of publication

Menlo Park

Event location

Philadelphia

Event date

Feb 27, 2025

Type of event by nationality

WRD - Celosvětová akce

UT code for WoS article

001477544600011