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On P versus NP∩co-NP for decision trees and read-once branching programs

Identifieur interne : 002A13 ( Main/Merge ); précédent : 002A12; suivant : 002A14

On P versus NP∩co-NP for decision trees and read-once branching programs

Auteurs : S. Jukna [Allemagne] ; A. Razborov [Russie] ; P. Savicky [République tchèque] ; I. Wegener [Allemagne]

Source :

Lecture notes in computer science [ 0302-9743 ] ; 1997.

RBID : Pascal:97-0493796

Descripteurs français

Pascal (Inist)
- Informatique théorique, Fonction booléenne, Arbre décision, Complexité calcul.

English descriptors

KwdEn :
- Boolean function, Computational complexity, Computer theory, Decision tree.

Abstract

It is known that if a Boolean function f in n variables has a DNF and a CNF of size < N then f also has a (deterministic) decision tree of size exp (O(log n log² N)). We show that this simulation cannot be made polynomial: we exhibit explicit Boolean functions f that require deterministic trees of size exp (Ω(log²N)) where N is the total number of monomials in minimal DNFs for and -f. Moreover, we exhibit new examples of explicit Boolean functions that require deterministic read-once branching programs of exponential size whereas both the functions and their negations have small nondeterministic read-once branching programs. One example results from the Bruen-Blokhuis bound on the size of nontrivial blocking sets in projective planes: it is remarkably simple and combinatorially clear. Whereas other examples have the additional property that is in AC°.

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Pascal:97-0493796

Le document en format XML

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<front><div type="abstract" xml:lang="en">It is known that if a Boolean function f in n variables has a DNF and a CNF of size < N then f also has a (deterministic) decision tree of size exp (O(log n log<sup>2</sup>
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N)) where N is the total number of monomials in minimal DNFs for and -f. Moreover, we exhibit new examples of explicit Boolean functions that require deterministic read-once branching programs of exponential size whereas both the functions and their negations have small nondeterministic read-once branching programs. One example results from the Bruen-Blokhuis bound on the size of nontrivial blocking sets in projective planes: it is remarkably simple and combinatorially clear. Whereas other examples have the additional property that is in AC°.</div>
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On P versus NP∩co-NP for decision trees and read-once branching programs

On P versus NP∩co-NP for decision trees and read-once branching programs

Source :

Descripteurs français

English descriptors

Abstract

Links toward previous steps (curation, corpus...)

Links to Exploration step

Le document en format XML

Pour manipuler ce document sous Unix (Dilib)

Pour mettre un lien sur cette page dans le réseau Wicri