Competitive Boolean function evaluation: Beyond monotonicity, and the symmetric case

  • Authors:
  • Ferdinando Cicalese;Travis Gagie;Eduardo Laber;Martin Milanič

  • Affiliations:
  • Dipartimento di Informatica ed Applicazioni, University of Salerno, Fisciano, Italy;Department of Computer Science, University of Chile, Santiago, Chile;Departamento de Informática, PUC-Rio, Rio De Janeiro, Brazil;PINT and FAMNIT, University of Primorska, Koper, Slovenia

  • Venue:
  • Discrete Applied Mathematics
  • Year:
  • 2011

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Abstract

We study the extremal competitive ratio of Boolean function evaluation. We provide the first non-trivial lower and upper bounds for classes of Boolean functions which are not included in the class of monotone Boolean functions. For the particular case of symmetric functions our bounds are matching and we exactly characterize the best possible competitiveness achievable by a deterministic algorithm. Our upper bound is obtained by a simple polynomial time algorithm.