DROPS

Document

DOI: 10.4230/LIPIcs.CP.2023.8

Symmetries for Cube-And-Conquer in Finite Model Finding

Authors: João Araújo, Choiwah Chow, and Mikoláš Janota

Published in: LIPIcs, Volume 280, 29th International Conference on Principles and Practice of Constraint Programming (CP 2023)

Abstract

The cube-and-conquer paradigm enables massive parallelization of SAT solvers, which has proven to be crucial in solving highly combinatorial problems. In this paper, we apply the paradigm in the context of finite model finding, where we show that isomorphic cubes can be discarded since they lead to isomorphic models. However, we are faced with the complication that a well-known technique, the Least Number Heuristic (LNH), already exists in finite model finders to effectively prune (some) isomorphic models from the search. Therefore, it needs to be shown that isomorphic cubes still can be discarded when the LNH is used. The presented ideas are incorporated into the finite model finder Mace4, where we demonstrate significant improvements in model enumeration.

Cite as

João Araújo, Choiwah Chow, and Mikoláš Janota. Symmetries for Cube-And-Conquer in Finite Model Finding. In 29th International Conference on Principles and Practice of Constraint Programming (CP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 280, pp. 8:1-8:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

Copy BibTex To Clipboard

@InProceedings{araujo_et_al:LIPIcs.CP.2023.8,
  author =	{Ara\'{u}jo, Jo\~{a}o and Chow, Choiwah and Janota, Mikol\'{a}\v{s}},
  title =	{{Symmetries for Cube-And-Conquer in Finite Model Finding}},
  booktitle =	{29th International Conference on Principles and Practice of Constraint Programming (CP 2023)},
  pages =	{8:1--8:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-300-3},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{280},
  editor =	{Yap, Roland H. C.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CP.2023.8},
  URN =		{urn:nbn:de:0030-drops-190455},
  doi =		{10.4230/LIPIcs.CP.2023.8},
  annote =	{Keywords: finite model enumeration, cube-and-conquer, symmetry-breaking, parallel algorithm, least number heuristic}
}

Document

Short Paper

DOI: 10.4230/LIPIcs.CP.2021.4

Filtering Isomorphic Models by Invariants (Short Paper)

Authors: João Araújo, Choiwah Chow, and Mikoláš Janota

Published in: LIPIcs, Volume 210, 27th International Conference on Principles and Practice of Constraint Programming (CP 2021)

Abstract

The enumeration of finite models of first order logic formulas is an indispensable tool in computational algebra. The task is hindered by the existence of isomorphic models, which are of no use to mathematicians and therefore are typically filtered out a posteriori. This paper proposes a divide-and-conquer approach to speed up and parallelize this process. We design a series of invariant properties that enable us to partition existing models into mutually non-isomorphic blocks, which are then tackled separately. The presented approach is integrated into the popular tool Mace4, where it shows tremendous speed-ups for a variety of algebraic structures.

Cite as

João Araújo, Choiwah Chow, and Mikoláš Janota. Filtering Isomorphic Models by Invariants (Short Paper). In 27th International Conference on Principles and Practice of Constraint Programming (CP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 210, pp. 4:1-4:9, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

Copy BibTex To Clipboard

@InProceedings{araujo_et_al:LIPIcs.CP.2021.4,
  author =	{Ara\'{u}jo, Jo\~{a}o and Chow, Choiwah and Janota, Mikol\'{a}\v{s}},
  title =	{{Filtering Isomorphic Models by Invariants}},
  booktitle =	{27th International Conference on Principles and Practice of Constraint Programming (CP 2021)},
  pages =	{4:1--4:9},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-211-2},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{210},
  editor =	{Michel, Laurent D.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CP.2021.4},
  URN =		{urn:nbn:de:0030-drops-152956},
  doi =		{10.4230/LIPIcs.CP.2021.4},
  annote =	{Keywords: finite model enumeration, isomorphism, invariants, Mace4}
}

Search Results

Documents authored by Araújo, João

Symmetries for Cube-And-Conquer in Finite Model Finding

Abstract

Cite as

Filtering Isomorphic Models by Invariants (Short Paper)

Abstract

Cite as

Thanks for your feedback!

Could not send message