On P versus NP∩co-NP for decision trees and read-once branching programs
Identifieur interne : 002474 ( Main/Exploration ); précédent : 002473; suivant : 002475On P versus NP∩co-NP for decision trees and read-once branching programs
Auteurs : S. Jukna [Allemagne] ; A. Razborov [Russie, Cuba] ; P. Savick [République tchèque, Swaziland] ; I. Wegener [Allemagne]Source :
- Lecture Notes in Computer Science [ 0302-9743 ] ; 1997.
Descripteurs français
- Pascal (Inist)
English descriptors
Abstract
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(log2 N)) where N is the total number of monomials in minimal DNFs for f 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 f is in AC°.
Url:
DOI: 10.1007/BFb0029975
Affiliations:
- Allemagne, Cuba, Russie, République tchèque, Swaziland
- Bohême centrale, District d'Arnsberg, District fédéral central, Rhénanie-Palatinat, Rhénanie-du-Nord-Westphalie
- Dortmund, Moscou, Prague, Trèves (Allemagne)
- Université de Trèves
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Le document en format XML
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