Binary Constraint Trees and Structured Decomposability

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F23%3A10477795" target="_blank" >RIV/00216208:11320/23:10477795 - isvavai.cz</a>

Result on the web

<a href="https://doi.org/10.4230/LIPIcs.CP.2023.22" target="_blank" >https://doi.org/10.4230/LIPIcs.CP.2023.22</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.4230/LIPIcs.CP.2023.22" target="_blank" >10.4230/LIPIcs.CP.2023.22</a>

Result language

angličtina

Original language name

Binary Constraint Trees and Structured Decomposability

Original language description

A binary constraint tree (BCT, Wang and Yap 2022) is a normalized binary CSP whose constraint graph is a tree. A BCT constraint is a constraint represented with a BCT where some of the variables may be hidden (i.e. existentially quantified and used only for internal representation). Structured decomposable negation normal forms (SDNNF) were introduced by Pipatsrisawat and Darwiche (2008) as a restriction of decomposable negation normal forms (DNNF). Both DNNFs and SDNNFs were studied in the area of knowledge compilation. In this paper we show that the BCT constraints are polynomially equivalent to SDNNFs. In particular, a BCT constraint can be represented with an SDNNF of polynomial size and, on the other hand, a constraint that can be represented with an SDNNF, can be represented as a BCT constraint of polynomial size. This generalizes the result of Wang and Yap (2022) that shows that a multivalued decision diagram (MDD) can be represented with a BCT. Moreover, our result provides a full characterization of binary constraint trees using a language that is well studied in the area of knowledge compilation. It was shown by Wang and Yap (2023) that a CSP on n variables of domain sizes bounded by d that has treewidth k can be encoded as a BCT on O(n) variables with domain sizes O(dk+1). We provide an alternative reduction for the case of binary CSPs. This allows us to compile any binary CSP to an SDNNF of size that is parameterized by d and k.

Czech name

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Czech description

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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)

Project

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Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2023

Confidentiality

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

Article name in the collection

Leibniz International Proceedings in Informatics, LIPIcs

ISBN

978-3-95977-300-3

ISSN

1868-8969

e-ISSN

—

Number of pages

19

Pages from-to

1-19

Publisher name

Schloss-Dagstuhl - Leibniz Zentrum für Informatik

Place of publication

Neuveden

Event location

Toronto, Canada

Event date

Aug 27, 2023

Type of event by nationality

WRD - Celosvětová akce

UT code for WoS article

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