Testing monotone read-once functions

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Abstract

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). © 2011 Springer-Verlag.

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Chistikov, D. V. (2011). Testing monotone read-once functions. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 7056 LNCS, pp. 121–134). https://doi.org/10.1007/978-3-642-25011-8_10

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