On the upper bounds for complexities of discrete functions
In this paper, we study two classes of complexity measures induced by new data structures (abstract reduction systems) for representing [Formula: see text]-valued functions (operations), namely subfunction and minor reductions. When assigning values to some variables in a function, the resulting functions are called subfunctions, and when identifying some variables, the resulting functions are called minors. The number of the distinct objects obtained under these reductions of a function [Formula: see text] is a well-defined measure of complexity denoted by [Formula: see text] and [Formula: see text], respectively. We examine the maximums of these complexities and construct functions which reach these upper bounds.
2019 ◽
Vol 30
(06n07)
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pp. 921-957
2019 ◽
Vol 55
(5)
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pp. 752-759
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2020 ◽
Vol ahead-of-print
(ahead-of-print)
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Keyword(s):
2010 ◽
Vol 24
(2)
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pp. 131-135
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Keyword(s):
2018 ◽
Vol 26
(3)
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pp. 115-140
2015 ◽
Vol E98.A
(1)
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pp. 39-48