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On deterministic approximation of DNF

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Abstract

We develop several quasi-polynomial-time deterministic algorithms for approximating the fraction of truth assignments that satisfy a disjunctive normal form formula. The most efficient algorithm computes for a given DNF formulaF onn variables withm clauses and ε > 0 an estimateY such that ¦Pr[F] −Y¦≤ε in time which is\((m\log (n))^{\exp (O(\sqrt {\log \log (m)} ))}\), for any constantε. Although the algorithms themselves are deterministic, their analysis is probabilistic and uses the notion of limited independence between random variables.

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Authors and Affiliations

  1. International Computer Science Institute, Berkeley

    M. Luby

  2. University of California, 94720, Berkeley, CA, USA

    M. Luby

  3. Equipe de Logique, Université Paris VII, Paris, France

    B. Veličković

Authors
  1. M. Luby
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  2. B. Veličković
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Additional information

Communicated by M. Luby.

Research supported in part by National Science Foundation Operating Grant CCR-9016468, National Science Foundation Operating Grant CCR-9304722, United States-Israel Binational Science Foundation Grant No. 89-00312, United States-Israel Binational Science Foundation Grant No. 92-00226, and ESPRIT Basic Research Grant EC-US 030.

Research partially done while visiting the International Computer Science Institute and while at Carnegie Mellon University.

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Luby, M., Veličković, B. On deterministic approximation of DNF. Algorithmica 16, 415–433 (1996). https://doi.org/10.1007/BF01940873

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  • DOI: https://doi.org/10.1007/BF01940873

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