Topic
Boolean function
About: Boolean function is a research topic. Over the lifetime, 10089 publications have been published within this topic receiving 201604 citations. The topic is also known as: Boolean operation.
Papers published on a yearly basis
1 / 2
Papers
1 Sep 1991
TL;DR: It turns out that, for any constant depth d, polynomial size sigmoid threshold circuits with polynomially bounded weights compute exactly the same Boolean functions as the corresponding circuits with Boolean threshold gates.
Abstract: The power of constant depth circuits with sigmoid (i.e., smooth) threshold gates for computing Boolean functions is examined. It is shown that, for depth 2, constant size circuits of this type are strictly more powerful than constant size Boolean threshold circuits (i.e., circuits with Boolean threshold gates). On the other hand it turns out that, for any constant depth d, polynomial size sigmoid threshold circuits with polynomially bounded weights compute exactly the same Boolean functions as the corresponding circuits with Boolean threshold gates. >
116 citations
TL;DR: It is shown that if a Boolean function has correlation at most e 1/2 with either of these models, then the correlation of the parity of its values on m independent instances drops exponentially with m, and for polynomials over GF(2) of degree d, the correlation drops to exp m/4 d.
Abstract: This paper presents a unified and simple treatment of basic questions concern- ing two computational models: multiparty communication complexity and polynomials over GF(2). The key is the use of (known) norms on Boolean functions, which capture their proximity to each of these models (and are closely related to property testers of this proximity). The main contributions are new XOR lemmas. We show that if a Boolean function has correlation at most e 1/2 with either of these models, then the correlation of the parity of its values on m independent instances drops exponentially with m. More specifically: • For polynomials over GF(2) of degree d, the correlation drops to exp m/4 d . No
116 citations
TL;DR: This paper introduces a new variant of this algorithm, where the Riemannian metric used for defining the search region is dynamically modified, and gives a method to synthesize a Boolean function that describes the sample.
Abstract: In this paper we describe an interior point mathematical programming approach to inductive inference. We list several versions of this problem and study in detail the formulation based on hidden Boolean logic. We consider the problem of identifying a hidden Boolean functionź:{0, 1}n ź {0, 1} using outputs obtained by applying a limited number of random inputs to the hidden function. Given this input--output sample, we give a method to synthesize a Boolean function that describes the sample. We pose the Boolean Function Synthesis Problem as a particular type of Satisfiability Problem. The Satisfiability Problem is translated into an integer programming feasibility problem, that is solved with an interior point algorithm for integer programming. A similar integer programming implementation has been used in a previous study to solve randomly generated instances of the Satisfiability Problem. In this paper we introduce a new variant of this algorithm, where the Riemannian metric used for defining the search region is dynamically modified. Computational results on 8-, 16- and 32-input, 1-output functions are presented. Our implementation successfully identified the majority of hidden functions in the experiment.
116 citations
TL;DR: In this article, the spin valves together with the recently discovered giant spin-Hall effect were used to construct Read and Write units that can be integrated into a single spin switch with input-output isolation, gain and fan-out similar to complementary metal oxide semiconductor inverters, but with the information stored in nanomagnets making it nonvolatile.
Abstract: We show that the established physics of spin valves together with the recently discovered giant spin-Hall effect could be used to construct Read and Write units that can be integrated into a single spin switch with input-output isolation, gain and fan-out similar to complementary metal oxide semiconductor inverters, but with the information stored in nanomagnets making it non-volatile. Such spin switches could be interconnected, with no external amplification, just with passive circuit elements, to perform logic operations. Moreover, since the digitization and storage occur naturally in the magnets, the voltages can be used to implement analog “weighting” for non-Boolean logic.
115 citations
TL;DR: This article demonstrates that the highly nonlinear permutation f(x)=x^2^^^2^k^+^ 2^^^k+^1 on the field F"2" ^"4"^"k, discovered by Hans Dobbertin (1998), has differential uniformity of four and hence, with respect to differential and linear cryptanalysis, is just as suitable for use in a symmetric cryptosystem as the inverse function.
115 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2026 | 3 |
| 2025 | 85 |
| 2024 | 130 |
| 2023 | 258 |
| 2022 | 454 |
| 2021 | 278 |