Binary Constraint Trees and Structured Decomposability
Identifikátory výsledku
Kód výsledku v 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>
Výsledek na webu
<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>
Alternativní jazyky
Jazyk výsledku
angličtina
Název v původním jazyce
Binary Constraint Trees and Structured Decomposability
Popis výsledku v původním jazyce
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.
Název v anglickém jazyce
Binary Constraint Trees and Structured Decomposability
Popis výsledku anglicky
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.
Klasifikace
Druh
D - Stať ve sborníku
CEP obor
—
OECD FORD obor
10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)
Návaznosti výsledku
Projekt
—
Návaznosti
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Ostatní
Rok uplatnění
2023
Kód důvěrnosti údajů
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Údaje specifické pro druh výsledku
Název statě ve sborníku
Leibniz International Proceedings in Informatics, LIPIcs
ISBN
978-3-95977-300-3
ISSN
1868-8969
e-ISSN
—
Počet stran výsledku
19
Strana od-do
1-19
Název nakladatele
Schloss-Dagstuhl - Leibniz Zentrum für Informatik
Místo vydání
Neuveden
Místo konání akce
Toronto, Canada
Datum konání akce
27. 8. 2023
Typ akce podle státní příslušnosti
WRD - Celosvětová akce
Kód UT WoS článku
—