2,001 research outputs found
Boolean Functions: Theory, Algorithms, and Applications
This monograph provides the first comprehensive presentation of the theoretical, algorithmic and applied aspects of Boolean functions, i.e., {0,1}-valued functions of a finite number of {0,1}-valued variables.
The book focuses on algebraic representations of Boolean functions, especially normal form representations. It presents the fundamental elements of the theory (Boolean equations and satisfiability problems, prime implicants and associated representations, dualization, etc.), an in-depth study of special classes of Boolean functions (quadratic, Horn, shellable, regular, threshold, read-once, etc.), and two fruitful generalizations of the concept of Boolean functions (partially defined and pseudo-Boolean functions). It features a rich bibliography of about one thousand items.
Prominent among the disciplines in which Boolean methods play a significant role are propositional logic, combinatorics, graph and hypergraph theory, complexity theory, integer programming, combinatorial optimization, game theory, reliability theory, electrical and computer engineering, artificial intelligence, etc. The book contains applications of Boolean functions in all these areas
Automatic Algorithm Selection for Pseudo-Boolean Optimization with Given Computational Time Limits
Machine learning (ML) techniques have been proposed to automatically select
the best solver from a portfolio of solvers, based on predicted performance.
These techniques have been applied to various problems, such as Boolean
Satisfiability, Traveling Salesperson, Graph Coloring, and others.
These methods, known as meta-solvers, take an instance of a problem and a
portfolio of solvers as input. They then predict the best-performing solver and
execute it to deliver a solution. Typically, the quality of the solution
improves with a longer computational time. This has led to the development of
anytime selectors, which consider both the instance and a user-prescribed
computational time limit. Anytime meta-solvers predict the best-performing
solver within the specified time limit.
Constructing an anytime meta-solver is considerably more challenging than
building a meta-solver without the "anytime" feature. In this study, we focus
on the task of designing anytime meta-solvers for the NP-hard optimization
problem of Pseudo-Boolean Optimization (PBO), which generalizes Satisfiability
and Maximum Satisfiability problems. The effectiveness of our approach is
demonstrated via extensive empirical study in which our anytime meta-solver
improves dramatically on the performance of Mixed Integer Programming solver
Gurobi, which is the best-performing single solver in the portfolio. For
example, out of all instances and time limits for which Gurobi failed to find
feasible solutions, our meta-solver identified feasible solutions for 47% of
these
ARPA Whitepaper
We propose a secure computation solution for blockchain networks. The
correctness of computation is verifiable even under malicious majority
condition using information-theoretic Message Authentication Code (MAC), and
the privacy is preserved using Secret-Sharing. With state-of-the-art multiparty
computation protocol and a layer2 solution, our privacy-preserving computation
guarantees data security on blockchain, cryptographically, while reducing the
heavy-lifting computation job to a few nodes. This breakthrough has several
implications on the future of decentralized networks. First, secure computation
can be used to support Private Smart Contracts, where consensus is reached
without exposing the information in the public contract. Second, it enables
data to be shared and used in trustless network, without disclosing the raw
data during data-at-use, where data ownership and data usage is safely
separated. Last but not least, computation and verification processes are
separated, which can be perceived as computational sharding, this effectively
makes the transaction processing speed linear to the number of participating
nodes. Our objective is to deploy our secure computation network as an layer2
solution to any blockchain system. Smart Contracts\cite{smartcontract} will be
used as bridge to link the blockchain and computation networks. Additionally,
they will be used as verifier to ensure that outsourced computation is
completed correctly. In order to achieve this, we first develop a general MPC
network with advanced features, such as: 1) Secure Computation, 2) Off-chain
Computation, 3) Verifiable Computation, and 4)Support dApps' needs like
privacy-preserving data exchange
Minimal approach to neuro-inspired information processing
© 2015 Soriano, Brunner, Escalona-Morán, Mirasso and Fischer. To learn and mimic how the brain processes information has been a major research challenge for decades. Despite the efforts, little is known on how we encode, maintain and retrieve information. One of the hypothesis assumes that transient states are generated in our intricate network of neurons when the brain is stimulated by a sensory input. Based on this idea, powerful computational schemes have been developed. These schemes, known as machine-learning techniques, include artificial neural networks, support vector machine and reservoir computing, among others. In this paper, we concentrate on the reservoir computing (RC) technique using delay-coupled systems. Unlike traditional RC, where the information is processed in large recurrent networks of interconnected artificial neurons, we choose a minimal design, implemented via a simple nonlinear dynamical system subject to a self-feedback loop with delay. This design is not intended to represent an actual brain circuit, but aims at finding the minimum ingredients that allow developing an efficient information processor. This simple scheme not only allows us to address fundamental questions but also permits simple hardware implementations. By reducing the neuro-inspired reservoir computing approach to its bare essentials, we find that nonlinear transient responses of the simple dynamical system enable the processing of information with excellent performance and at unprecedented speed. We specifically explore different hardware implementations and, by that, we learn about the role of nonlinearity, noise, system responses, connectivity structure, and the quality of projection onto the required high-dimensional state space. Besides the relevance for the understanding of basic mechanisms, this scheme opens direct technological opportunities that could not be addressed with previous approaches.The authors acknowledge support by MINECO (Spain) under Projects TEC2012-36335 (TRIPHOP) and FIS2012-30634 (Intense@cosyp), FEDER and Govern de les Illes Balears via the program Grups Competitius. The work of MS was supported by the Conselleria d'Educació, Cultura i Universitats del Govern de les Illes Balears and the European Social Fund.Peer Reviewe
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