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
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Papers
TL;DR: Two new binarization approaches are introduced which determine thresholds based on limited numbers of samples and additionally provide a measure of threshold validity, which reduces the complexity of network inference.
Abstract: Network inference algorithms can assist life scientists in unraveling gene-regulatory systems on a molecular level. In recent years, great attention has been drawn to the reconstruction of Boolean networks from time series. These need to be binarized, as such networks model genes as binary variables (either "expressed” or "not expressed”). Common binarization methods often cluster measurements or separate them according to statistical or information theoretic characteristics and may require many data points to determine a robust threshold. Yet, time series measurements frequently comprise only a small number of samples. To overcome this limitation, we propose a binarization that incorporates measurements at multiple resolutions. We introduce two such binarization approaches which determine thresholds based on limited numbers of samples and additionally provide a measure of threshold validity. Thus, network reconstruction and further analysis can be restricted to genes with meaningful thresholds. This reduces the complexity of network inference. The performance of our binarization algorithms was evaluated in network reconstruction experiments using artificial data as well as real-world yeast expression time series. The new approaches yield considerably improved correct network identification rates compared to other binarization techniques by effectively reducing the amount of candidate networks.
75 citations
TL;DR: This article considers a Mayer-type optimal control problem of probabilistic Boolean control networks (PBCNs) with uncertainty on selection probabilities which obey Beta Probabilistic distributions and deduces an equivalent formulation as a multistage decision problem.
Abstract: This article considers a Mayer-type optimal control problem of probabilistic Boolean control networks (PBCNs) with uncertainty on selection probabilities which obey Beta probabilistic distributions. The expectation with respect to both the selection probabilities and the transitions of state variables is set as a cost function, and it deduces an equivalent formulation as a multistage decision problem. Furthermore, the dynamic programming technique is applied to solve the problem and performs a novel optimization algorithm in the fashion of semitensor product. A numerical example of a biological model of apoptosis protein demonstrates the effectiveness and feasibility of the proposed framework and algorithms.
75 citations
TL;DR: This paper investigates single electron encoded logic (SEEL) memory circuits, in which the Boolean logic values are encoded as zero or one electron charges, and presents a generic SEEL linear threshold gate implementation, from which a family of Boolean logic gates are derived.
Abstract: Single electron tunneling (SET) technology offers the ability to control the transport of individual electrons. In this paper, we investigate single electron encoded logic (SEEL) memory circuits, in which the Boolean logic values are encoded as zero or one electron charges. More specifically, we focus on the implementation of SEEL latches and flip-flops. All proposed circuits are verified by means of simulation using the SIMulation Of Nanostructures package. We first present a generic SEEL linear threshold gate implementation, from which we derive a family of Boolean logic gates. Second, we propose Boolean gate-based implementations of the RS latch, the D latch, and D flip-flop. Third, we propose threshold gate-based implementations of the same memory elements. Finally, we discuss the estimated area, delay, and power consumption of the Boolean gate-based and threshold gate-based implementations, and compare them with other SET-based memory elements.
74 citations
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TL;DR: This work presents, so called, semi-bent functions which satisfy all of these properties of high nonlinear balanced Boolean functions, both satisfying the propagation criterion and having almost uniform correlation values with all linear functions.
Abstract: Highly nonlinear balanced Boolean functions both satisfying the propagation criterion and having almost uniform correlation values with all linear functions are very important in the design of hash functions, stream and block ciphers. In particular, the output uncorrelated properties between two Boolean functions are required to design permutations. We present, so called, semi-bent functions which satisfy all of these properties.
74 citations
20 Aug 2006
TL;DR: It is deduced that it is enough, for a Boolean function, to have high algebraic immunity, for having non-weak low order nonlinearity profile (even when it cannot be evaluated), except maybe for the first order.
Abstract: One of the most basic requirements concerning Boolean functions used in cryptosystems is that they must have high algebraic degrees. This simple criterion is not always well adapted to the concrete situation in which Boolean functions are used in symmetric cryptography, since changing one or several output bits of a Boolean function considerably changes its algebraic degree while it may not change its robustness. The proper characteristic is the r-th order nonlinearity profile (which includes the first-order nonlinearity). However, studying it is difficult and almost no paper, in the literature, has ever been able to give general effective results on it. The values of the nonlinearity profile are known for very few functions and these functions have little cryptographic interest. A recent paper has given a lower bound on the nonlinearity profile of functions, given their algebraic immunity. We improve upon it, and we deduce that it is enough, for a Boolean function, to have high algebraic immunity, for having non-weak low order nonlinearity profile (even when it cannot be evaluated), except maybe for the first order.
74 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2026 | 3 |
| 2025 | 85 |
| 2024 | 130 |
| 2023 | 258 |
| 2022 | 454 |
| 2021 | 278 |