Testing Monotone Read-Once Functions

  • Dmitry V. Chistikov
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7056)


A checking test for a monotone read-once function f depending essentially on all its n variables is a set of vectors M distinguishing f from all other monotone read-once functions of the same variables. We describe an inductive procedure for obtaining individual lower and upper bounds on the minimal number of vectors T(f) in a checking test for any function f. The task of deriving the exact value of T(f) is reduced to a combinatorial optimization problem related to graph connectivity. We show that for almost all functions f expressible by read-once conjunctive or disjunctive normal forms, T(f) ~n / ln n. For several classes of functions our results give the exact value of T(f).


Equivalence Relation Boolean Function Combinatorial Optimization Problem Inductive Assumption Conjunctive Normal Form 
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© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Dmitry V. Chistikov
    • 1
  1. 1.Faculty of Computational Mathematics and CyberneticsMoscow State UniversityRussia

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