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.

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TL;DR: In this paper, the authors present a data structure for representing Boolean functions and an associated set of manipulation algorithms, which have time complexity proportional to the sizes of the graphs being operated on, and hence are quite efficient as long as the graphs do not grow too large.

Abstract: In this paper we present a new data structure for representing Boolean functions and an associated set of manipulation algorithms. Functions are represented by directed, acyclic graphs in a manner similar to the representations introduced by Lee [1] and Akers [2], but with further restrictions on the ordering of decision variables in the graph. Although a function requires, in the worst case, a graph of size exponential in the number of arguments, many of the functions encountered in typical applications have a more reasonable representation. Our algorithms have time complexity proportional to the sizes of the graphs being operated on, and hence are quite efficient as long as the graphs do not grow too large. We present experimental results from applying these algorithms to problems in logic design verification that demonstrate the practicality of our approach.

8,721 citations

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22 Jun 2001

TL;DR: The development of a new complete solver, Chaff, is described which achieves significant performance gains through careful engineering of all aspects of the search-especially a particularly efficient implementation of Boolean constraint propagation (BCP) and a novel low overhead decision strategy.

Abstract: Boolean satisfiability is probably the most studied of the combinatorial optimization/search problems. Significant effort has been devoted to trying to provide practical solutions to this problem for problem instances encountered in a range of applications in electronic design automation (EDA), as well as in artificial intelligence (AI). This study has culminated in the development of several SAT packages, both proprietary and in the public domain (e.g. GRASP, SATO) which find significant use in both research and industry. Most existing complete solvers are variants of the Davis-Putnam (DP) search algorithm. In this paper we describe the development of a new complete solver, Chaff which achieves significant performance gains through careful engineering of all aspects of the search-especially a particularly efficient implementation of Boolean constraint propagation (BCP) and a novel low overhead decision strategy. Chaff has been able to obtain one to two orders of magnitude performance improvement on difficult SAT benchmarks in comparison with other solvers (DP or otherwise), including GRASP and SATO.

2,782 citations

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TL;DR: It is shown that a class of deterministic lattice gases with discrete Boolean elements simulates the Navier-Stokes equation, anc, and can be used to design simple, massively parallel computing machines.

Abstract: We show that a class of deterministic lattice gases with discrete Boolean elements simulates the Navier-Stokes equation, anc can be used to design simple, massively parallel computing machines.

2,207 citations

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TL;DR: In this paper, the authors investigate the use of data-dependent estimates of the complexity of a function class, called Rademacher and Gaussian complexities, in a decision theoretic setting and prove general risk bounds in terms of these complexities.

Abstract: We investigate the use of certain data-dependent estimates of the complexity of a function class, called Rademacher and Gaussian complexities. In a decision theoretic setting, we prove general risk bounds in terms of these complexities. We consider function classes that can be expressed as combinations of functions from basis classes and show how the Rademacher and Gaussian complexities of such a function class can be bounded in terms of the complexity of the basis classes. We give examples of the application of these techniques in finding data-dependent risk bounds for decision trees, neural networks and support vector machines.

2,201 citations

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TL;DR: The OBDD data structure is described and a number of applications that have been solved by OBDd-based symbolic analysis are surveyed.

Abstract: Ordered Binary-Decision Diagrams (OBDDs) represent Boolean functions as directed acyclic graphs. They form a canonical representation, making testing of functional properties such as satisfiability and equivalence straightforward. A number of operations on Boolean functions can be implemented as graph algorithms on OBDD data structures. Using OBDDs, a wide variety of problems can be solved through symbolic analysis. First, the possible variations in system parameters and operating conditions are encoded with Boolean variables. Then the system is evaluated for all variations by a sequence of OBDD operations. Researchers have thus solved a number of problems in digital-system design, finite-state system analysis, artificial intelligence, and mathematical logic. This paper describes the OBDD data structure and surveys a number of applications that have been solved by OBDD-based symbolic analysis.

2,128 citations