UnivTrevesV1, PascalFrancis, Corpus, bibRecord, 001360

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

Identifieur interne : 001360 ( PascalFrancis/Corpus ); précédent : 001359; suivant : 001361

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

Auteurs : S. Jukna ; A. Razborov ; P. Savicky ; I. Wegener

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°.

Notice en format standard (ISO 2709)

Pour connaître la documentation sur le format Inist Standard.

A01	`01`	`1`		`@0 0302-9743`
A05				`@2 1295`
A08	`01`	`1`	`ENG`	`@1 On P versus NP∩co-NP for decision trees and read-once branching programs`
A09	`01`	`1`	`ENG`	`@1 MFCS '97 : mathematical foundations of computer science 1997 : Bratislava, August 25-29, 1997`
A11	`01`	`1`		`@1 JUKNA (S.)`
A11	`02`	`1`		`@1 RAZBOROV (A.)`
A11	`03`	`1`		`@1 SAVICKY (P.)`
A11	`04`	`1`		`@1 WEGENER (I.)`
A12	`01`	`1`		`@1 PRIVARA (Igor) @9 ed.`
A12	`02`	`1`		`@1 RUZICKA (Peter) @9 ed.`
A14	`01`			`@1 Dept. of Computer Science, University of Trier @2 54286 Trier @3 DEU @Z 1 aut.`
A14	`02`			`@1 Steklov Mathematical Institute, Gubkina 8 @2 117966, Moscow @3 RUS @Z 2 aut.`
A14	`03`			`@1 Institute of Computer Science. Acad. of Sci. of Czech Republic. Pod vodárenskou vezi 2 @2 182 07 Praha @3 CZE @Z 3 aut.`
A14	`04`			`@1 Dept. of Computer Science. University of Dortmund @2 44221 Dortmund @3 DEU @Z 4 aut.`
A20				`@1 319-326`
A21				`@1 1997`
A23	`01`			`@0 ENG`
A26	`01`			`@0 3-540-63437-1`
A43	`01`			`@1 INIST @2 16343 @5 354000068068640320`
A44				`@0 0000 @1 © 1997 INIST-CNRS. All rights reserved.`
A45				`@0 19 ref.`
A47	`01`	`1`		`@0 97-0493796`
A60				`@1 P @2 C`
A61				`@0 A`
A64	`01`	`1`		`@0 Lecture notes in computer science`
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A66	`02`			`@0 USA`
C01	`01`		`ENG`	@0 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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C03	`01`	`X`	`FRE`	`@0 Informatique théorique @5 01`
C03	`01`	`X`	`ENG`	`@0 Computer theory @5 01`
C03	`01`	`X`	`SPA`	`@0 Informática teórica @5 01`
C03	`02`	`X`	`FRE`	`@0 Fonction booléenne @5 02`
C03	`02`	`X`	`ENG`	`@0 Boolean function @5 02`
C03	`02`	`X`	`SPA`	`@0 Función booliana @5 02`
C03	`03`	`X`	`FRE`	`@0 Arbre décision @5 03`
C03	`03`	`X`	`ENG`	`@0 Decision tree @5 03`
C03	`03`	`X`	`SPA`	`@0 Arbol decisión @5 03`
C03	`04`	`X`	`FRE`	`@0 Complexité calcul @5 04`
C03	`04`	`X`	`ENG`	`@0 Computational complexity @5 04`
C03	`04`	`X`	`SPA`	`@0 Complejidad computación @5 04`
N21				`@1 300`

A30	`01`	`1`	`ENG`	`@1 Mathematical foundations of computer science. International symposium @2 22 @3 Bratislava SVK @4 1997-08-25`

Format Inist (serveur)

NO :	PASCAL 97-0493796 INIST
ET :	On P versus NP∩co-NP for decision trees and read-once branching programs
AU :	JUKNA (S.); RAZBOROV (A.); SAVICKY (P.); WEGENER (I.); PRIVARA (Igor); RUZICKA (Peter)
AF :	Dept. of Computer Science, University of Trier/54286 Trier/Allemagne (1 aut.); Steklov Mathematical Institute, Gubkina 8/117966, Moscow/Russie (2 aut.); Institute of Computer Science. Acad. of Sci. of Czech Republic. Pod vodárenskou vezi 2/182 07 Praha/Tchèque, République (3 aut.); Dept. of Computer Science. University of Dortmund/44221 Dortmund/Allemagne (4 aut.)
DT :	Publication en série; Congrès; Niveau analytique
SO :	Lecture notes in computer science; ISSN 0302-9743; Allemagne; Da. 1997; Vol. 1295; Pp. 319-326; Bibl. 19 ref.
LA :	Anglais
EA :	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°.
CC :	001D02A04
FD :	Informatique théorique; Fonction booléenne; Arbre décision; Complexité calcul
ED :	Computer theory; Boolean function; Decision tree; Computational complexity
SD :	Informática teórica; Función booliana; Arbol decisión; Complejidad computación
LO :	INIST-16343.354000068068640320
ID :	97-0493796

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Pascal:97-0493796

Le document en format XML

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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

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Abstract

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Format Inist (serveur)

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Le document en format XML

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