Connecting Knowledge Compilation Classes and Width Parameters

Amarilli, Antoine; Capelli, Florent; Monet, Mikaël; Senellart, Pierre

Document type :

Compte-rendu et recension critique d'ouvrage

DOI :

10.1007/s00224-019-09930-2

Title :

Connecting Knowledge Compilation Classes and Width Parameters

Author(s) :

Amarilli, Antoine [Auteur]
Data, Intelligence and Graphs [DIG]
Capelli, Florent [Auteur]

Linking Dynamic Data [LINKS]
Monet, Mikaël [Auteur]
Data, Intelligence and Graphs [DIG]
Senellart, Pierre [Auteur]
Value from Data [VALDA]
Data, Intelligence and Graphs [DIG]

Journal title :

Theory of Computing Systems

Publisher :

Springer Verlag

Publication date :

2020-08-01

ISSN :

1432-4350

English keyword(s) :

Boolean circuits
d-DNNFs
OBDDs
Pathwidth
Knowledge compilation
Treewidth

HAL domain(s) :

Informatique [cs]

English abstract : [en]

The field of knowledge compilation establishes the tractability of many tasks by studying how to compile them to Boolean circuit classes obeying some requirements such as structuredness, decomposability, and determinism. ...
Show more >The field of knowledge compilation establishes the tractability of many tasks by studying how to compile them to Boolean circuit classes obeying some requirements such as structuredness, decomposability, and determinism. However, in other settings such as intensional query evaluationon databases, we obtain Boolean circuits that satisfy some width bounds, e.g., they have bounded treewidth or pathwidth. In this work, we give a systematic picture of many circuit classes considered in knowledge compilation and show how they can be systematically connected to width measures, through upper and lower bounds. Our upper bounds show that boundedtreewidth circuits can be constructively converted to d-SDNNFs, in time linear in the circuit size and singly exponential in the treewidth; and that bounded-pathwidth circuits can similarly be converted to uOBDDs. We show matching lower bounds on the compilation of monotone DNF or CNF formulas to structured targets, assuming a constant bound on the arity (size of clauses) and degree (number of occurrences of each variable): any d-SDNNF (resp., SDNNF) for such a DNF (resp., CNF) must be of exponential size in its treewidth, and the same holds for uOBDDs (resp., n-OBDDs) when considering pathwidth. Unlike most previous work, our bounds apply to any formula of this class, not just a well-chosen family. Hence, we show that pathwidth and treewidth respectively characterize the efficiency of compiling monotone DNFs to uOBDDs and d-SDNNFs with compilation being singly exponential in the corresponding width parameter. We also show that our lower bounds on CNFs extend to unstructured compilation targets, with an exponential lower bound in the treewidth (resp., pathwidth) when compiling monotone CNFs of constant arity and degree to DNNFs (resp., nFBDDs).Show less >

Language :

Anglais

Popular science :

Non

ANR Project :

Requêtes d'Agrégation

Collections :