Checking Tests for Read-Once Functions over Arbitrary Bases

  • Dmitry V. Chistikov
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7353)


A Boolean function is called read-once over a basis B if it can be expressed by a formula over B where no variable appears more than once. A checking test for a read-once function f over B depending on all its variables is a set of input vectors distinguishing f from all other read-once functions of the same variables. We show that every read-once function f over B has a checking test containing O(n l ) vectors, where n is the number of relevant variables of f and l is the largest arity of functions in B. For some functions, this bound cannot be improved by more than a constant factor. The employed technique involves reconstructing f from its l-variable projections and provides a stronger form of Kuznetsov’s classic theorem on read-once representations.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

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

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