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

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Mathematical Foundations of Computer Science 1997 (MFCS 1997)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1295))

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°.

Supported by DFG grant Me 1077/101. On leave from Institute of Mathematics, Vilnius, Lithuania.

Supported by RBRF grant #96-01-01222.

Supported by grant of GA the Czech Republic No. 201/95/0976.

Supported by DFG grant We 1066/8-1.

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Author information

Authors and Affiliations

  1. Dept. of Computer Science, University of Trier, D-54286, Trier, Germany

    S. Jukna

  2. Steklov Mathematical Institute, Gubkina 8, 117966, Moscow, Russia

    A. Razborov

  3. Acad. of Sci. of Czech Republic, Institute of Computer Science, Pod vodárenskou věží 2, 182 07, Praha 8, Czech Republic

    P. Savický

  4. Dept. of Computer Science, University of Dortmund, D-44221, Dortmund, Germany

    I. Wegener

Authors
  1. S. Jukna
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  2. A. Razborov
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  3. P. Savický
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  4. I. Wegener
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Igor Prívara Peter Ružička

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© 1997 Springer-Verlag Berlin Heidelberg

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Jukna, S., Razborov, A., Savický, P., Wegener, I. (1997). On P versus NP∩co-NP for decision trees and read-once branching programs. In: Prívara, I., Ružička, P. (eds) Mathematical Foundations of Computer Science 1997. MFCS 1997. Lecture Notes in Computer Science, vol 1295. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0029975

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  • DOI: https://doi.org/10.1007/BFb0029975

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-63437-9

  • Online ISBN: 978-3-540-69547-9

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