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).
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Bubnov, S.E., Voronenko, A.A., Chistikov, D.V.: Some test length bounds for nonrepeating functions in the \(\{\&, \lor\}\) basis. Computational Mathematics and Modeling 21(2), 196–205 (2010)
Chistikov, D.V.: Testing read-once functions over the elementary basis. Moscow University Computational Mathematics and Cybernetics (to appear)
Corneil, D.G., Lerchs, H., Stewart Burlingham, L.: Complement reducible graphs. Discrete Applied Mathematics 3(3), 163–174 (1981)
Gurvich, V.A.: On repetition-free Boolean functions. Uspehi Matematicheskih nauk 32(1), 183–184 (1977) (in Russian)
Karchmer, M., Linial, N., Newman, I., Saks, M., Widgerson, A.: Combinatorial characterization of read-once formulae. Discrete Mathematics 114(1-3), 275–282 (1993)
Ryabets, L.V.: Checking test complexity for read-once Boolean functions. Ser. Diskretnaya matematika i informatika, vol. 18. Izdatel’stvo Irkutskogo gosudarstvennogo pedagogicheskogo universiteta (2007) (in Russian)
Sachkov, V.N.: Probabilistic methods in combinatorial analysis. Encyclopedia of Mathematics and its Applications, vol. 56. Cambridge University Press (1997)
Voronenko, A.A.: Estimating the length of a diagnostic test for some nonrepeating functions. Computational Mathematics and Modeling 15(4), 377–386 (2004)
Voronenko, A.A.: On checking tests for read-once functions. In: Matematicheskie Voprosy Kibernetiki, Fizmatlit, Moscow, vol. 11, pp. 163–176 (2002) (in Russian)
Voronenko, A.A.: On the length of checking test for repetition-free functions in the basis \(\{0, 1, \&, \lor, \neg\}\). Discrete Mathematics and Applications 15(3), 313–318 (2005)
Voronenko, A.A.: Recognizing the nonrepeating property in an arbitrary basis. Computational Mathematics and Modeling 18(1), 55–65 (2007)
Voronenko, A.A., Chistikov, D.V.: Learning read-once functions individually. Uchenye zapiski Kazanskogo universiteta. Ser. Fiziko-matematicheskie nauki 151(2), 36–44 (2009) (in Russian)
Voronenko, A.A., Chistikov, D.V.: On testing read-once Boolean functions in the basis B 5. In: Proceedings of the XVII International Workshop “Synthesis and complexity of control systems”, pp. 24–30. Izdatel stvo Instituta matematiki, Novosibirsk (2008) (in Russian)
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Chistikov, D.V. (2011). Testing Monotone Read-Once Functions. In: Iliopoulos, C.S., Smyth, W.F. (eds) Combinatorial Algorithms. IWOCA 2011. Lecture Notes in Computer Science, vol 7056. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25011-8_10
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DOI: https://doi.org/10.1007/978-3-642-25011-8_10
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