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On the Communication Complexity of AND Functions
IEEE Transactions on Information Theory, 2021Log-rank conjecture is one of challenging problems in communication complexity. It is known to hold for some special function classes such as XOR functions $\text {f}(\text {x}\oplus \text {y})$ when the outer function f is monotone, symmetric, $\mathsf {AC}^{0}$ , low $\mathbb {F}_{2}$ -degree, linear threshold or read-k.
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The complexity of AND—decomposition of Boolean functions
Discrete Applied Mathematics, 2020zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Pavel G. Emelyanov, Denis K. Ponomaryov
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Computational Methods and Function Theory, 2013
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On the complexity of proving functions
Proceedings of the November 16-18, 1971, fall joint computer conference on - AFIPS '71 (Fall), 1971Let f be a recursive function. We shall be interested in the following question: given x and y, how difficult is it to decide whether f(x) = y or f(x) ≠ y? Since the problem of deciding f(x) = y or f(x) ≠ y is the same problem as that of computing the characteristic function Cf of the graph of f, we can study the above question by looking into the ...
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Phosphoinositides in Golgi Complex Function
2012The Golgi complex is a ribbon-like organelle composed of stacks of flat cisternae interconnected by tubular junctions. It occupies a central position in the endomembrane system as proteins and lipids that are synthesized in the endoplasmic reticulum (ER) pass through the Golgi complex to undergo biosynthetic modification (mainly glycosylation) and to ...
D’Angelo, Giovanni +3 more
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Complex functions of the brain
Zoology, 2001Over the course of the last 50 years it has been possible to solve a number of basic problems in neurobiology. Interest is now turning more and more to problems concerning so-called "higher" brain functions, including cognition. Examples from the visual system in primates are presented.
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2016
We introduced complex numbers in Sect. 1.8 of the first volume. There we just defined the numbers themselves, but did not go any further. In fact, since the introduction of complex numbers a number of centuries ago, the theory based on them has been substantially developed into an extended analysis of complex functions defined on the complex plane. The
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We introduced complex numbers in Sect. 1.8 of the first volume. There we just defined the numbers themselves, but did not go any further. In fact, since the introduction of complex numbers a number of centuries ago, the theory based on them has been substantially developed into an extended analysis of complex functions defined on the complex plane. The
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On the complexity of balanced Boolean functions
Information Processing Letters, 1997zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On the Multiplicative Complexity of Boolean Functions
Fundamenta Informaticae, 2016The multiplicative complexity μ(f) of a Boolean function f is the smallest number of & (of AND gates) in circuits in the basis {x&y, x⊕y, 1} such that each circuit implements the function f. By μ(S) we denote the number of & (of AND gates) in a circuit S in the basis {x&y, x ⊕ y, 1}. We present a method to construct circuits in the basis {x&y, x ⊕ y, 1}
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