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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