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
7 Nov 2004
TL;DR: This work corrects the bad behavior of two-level optimization by devising a simple linear simplification algorithm that can remove tens of thousands of nodes on examples where all obvious redundancies already have been removed.
Abstract: The choice of representation for circuits and Boolean formulae in a formal verification tool is important for two reasons. First of all, representation compactness is necessary in order to keep the memory consumption low. This is witnessed by the importance of maximum processable design size for equivalence checkers. Second, many formal verification algorithms are sensitive to redundancies in the design that is processed. To address these concerns, three different auto-compressing representations for Boolean circuit networks and formulas have been suggested in the literature. We attempt to find a blend of features from these alternatives that allows us to remove as much redundancy as possible while not sacrificing runtime. By studying how the network representation size varies when we change parameters, we show that the use of only one operator node is suboptimal, and demonstrate that the most powerful of the proposed reduction rules, two-level minimization, actually can be harmful. We correct the bad behavior of two-level optimization by devising a simple linear simplification algorithm that can remove tens of thousands of nodes on examples where all obvious redundancies already have been removed. The combination of our compactor with the simplest representation outperforms all of the alternatives we have studied, with a theoretical runtime bound that is at least as good as the three studied representations.
107 citations
Journal Article•
TL;DR: A new technique for proving lower bounds in property testing is developed, by showing a strong connection between testing and communication complexity, and significantly strengthens the best known bounds.
Abstract: We develop a new technique for proving lower bounds in property testing, by showing a strong connection between testing and communication complexity. We give a simple scheme for reducing communication problems to testing problems, thus allowing us to use known lower bounds in communication complexity to prove lower bounds in testing. This scheme is general and implies a number of new testing bounds, as well as simpler proofs of several known bounds. For the problem of testing whether a boolean function is k-linear (a parity function on k variables), we achieve a lower bound of Omega(k) queries, even for adaptive algorithms with two-sided error, thus confirming a conjecture of Goldreich (2010). The same argument behind this lower bound also implies a new proof of known lower bounds for testing related classes such as k-juntas. For some classes, such as the class of monotone functions and the class of s-sparse GF(2) polynomials, we significantly strengthen the best known bounds.
107 citations
2 Sep 1991
TL;DR: An analytical model for the behavior of dataflow graphs with data-dependent control flow that can be analyzed to construct an annotated schedule, or a static schedule that annotates each firing of an actor with the Boolean conditions under which that firing occurs.
Abstract: This paper describes an analytical model for the behavior of dataflow graphs with data-dependent control flow. The number of tokens produced or consumed by each actor is given as a symbolic function of the Booleans in the system. Long term averages can be analyzed to determine consistency of token flow rates, which in turn determines whether memory requirements are bounded. Short-term behavior can be analyzed to construct an annotated schedule, or a static schedule that annotates each firing of an actor with the Boolean conditions under which that firing occurs. Annotated schedules can be used to generate efficient implementations of the algorithms given by the dataflow graphs. >
106 citations
TL;DR: The robust stability and stabilization of Boolean networks with stochastic function perturbations is studied and it is proved that the finite-time stability is reduced to stability in distribution when the intersection of perturbed set and complement set of parameterized set is nonempty.
Abstract: In genetic regulatory networks (GRNs), gene mutations often occur in a stochastic manner. As an important model of GRNs, gene mutations of Boolean networks are always described as function perturbations. This article studies the robust stability and stabilization of Boolean networks with stochastic function perturbations. A kind of parameterized set is constructed, and it is revealed that under the stochastic function perturbations, the property of finite-time stability remains unchanged when the perturbed set and the parameterized set are disjoint. In addition, it is proved that the finite-time stability is reduced to stability in distribution when the intersection of perturbed set and complement set of parameterized set is nonempty. As an application, the robust stabilization problem of Boolean control networks with stochastic function perturbations is discussed, and several necessary and sufficient conditions are presented for the robustness of feedback stabilizers. Finally, the obtained results are used to study the Drosophila melanogaster segmentation polarity gene network and the lac operon in the bacterium Escherichia coil.
106 citations
[...]
TL;DR: This paper reviews the recent research results beginning from the standard uncoupled CNN cell which can realize only linearly separable local Boolean functions, to a generalized universal CNN cell capable of realizing arbitrary Boolean functions.
Abstract: A cellular neural/nonlinear network (CNN) [Chua, 1998] is a biologically inspired system where computation emerges from a collection of simple nonlinear locally coupled cells. This paper reviews our recent research results beginning from the standard uncoupled CNN cell which can realize only linearly separable local Boolean functions, to a generalized universal CNN cell capable of realizing arbitrary Boolean functions. The key element in this evolutionary process is the replacement of the linear discriminant (offset) function w(σ)=σ in the "standard" CNN cell in [Chua, 1998] by a piecewise-linear function defined in terms of only absolute value functions. As in the case of the standard CNN cells, the excitation σ evaluates the correlation between a given input vector u formed by the outputs of the neighboring cells, and a template vector b, which is interpreted in this paper as an orientation vector. Using the theory of canonical piecewise-linear functions [Chua & Kang, 1977], the discriminant function is found to guarantee universality and its parameters can be easily determined. In this case, the number of additional parameters and absolute value functions m is bounded by m<2n-1, where n is the number of all inputs (n=9 for a 3×3 template). An even more compact representation where m
106 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2026 | 3 |
| 2025 | 85 |
| 2024 | 130 |
| 2023 | 258 |
| 2022 | 454 |
| 2021 | 278 |