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Closed Classes of Boolean Functions

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Part of the book series: Intelligent Systems Reference Library ((ISRL,volume 179))

Abstract

In this chapter, for decision tables corresponding to functions from an arbitrary closed class of Boolean functions, the depth of deterministic, nondeterministic, and strongly nondeterministic decision trees is studied. The obtained results have some independent interest. Proofs of these results illustrate mainly methods for the proof of lower bounds on complexity of decision trees.

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References

  1. Moshkov, M.: About the depth of decision trees computing Boolean functions. Fundam. Inform. 22(3), 203–215 (1995)

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  2. Moshkov, M.: Time complexity of decision trees. In: Peters, J.F., Skowron, A. (eds.) Transactions on Rough Sets III, Lecture Notes in Computer Science, vol. 3400, pp. 244–459. Springer, Berlin (2005)

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  3. Post, E.: Introduction to a general theory of elementary propositions. Am. J. Math. 43, 163–185 (1921)

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  4. Post, E.: Two-Valued Iterative Systems of Mathematical Logic. Annals of Mathematics Studies, vol. 5. Princeton University Press, Princeton-London (1941)

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  5. Yablonskii, S.V., Gavrilov, G.P., Kudriavtzev, V.B.: Functions of the Algebra of Logic and Post Classes. Nauka Publishers, Moscow (1966). (in Russian)

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Correspondence to Mikhail Moshkov .

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Moshkov, M. (2020). Closed Classes of Boolean Functions. In: Comparative Analysis of Deterministic and Nondeterministic Decision Trees. Intelligent Systems Reference Library, vol 179. Springer, Cham. https://doi.org/10.1007/978-3-030-41728-4_7

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