On a Theory of Boolean Functions
01 Dec 1959-Journal of The Society for Industrial and Applied Mathematics (Society for Industrial and Applied Mathematics)-Vol. 7, Iss: 4, pp 487-498
About: This article is published in Journal of The Society for Industrial and Applied Mathematics.The article was published on 1959-12-01. It has received 201 citations till now. The article focuses on the topics: Boolean expression & Boolean algebras canonically defined.
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01 Jan 2009TL;DR: In this paper, the authors define testing as the process of applying a few well-defined, general-purpose test criteria to a structure or model of the software, and present an innovative approach to explaining the process.
Abstract: Extensively class tested, this text takes an innovative approach to explaining the process of software testing: it defines testing as the process of applying a few well-defined, general-purpose test criteria to a structure or model of the software. The structure of the text directly reflects the pedagogical approach and incorporates the latest innovations in testing, including techniques to test modern types of software such as OO, web applications, and embedded software.
1,126 citations
01 Jan 2008
TL;DR: The structure of the text directly reflects the pedagogical approach and incorporates the latest innovations in testing, including techniques to test modern types of software such as OO, web applications and embedded software.
Abstract: Extensively class tested, this text takes an innovative approach to explaining the process of software testing: it defines testing as the process of applying a few well-defined, general-purpose test criteria to a structure or model of the software. The structure of the text directly reflects the pedagogical approach and incorporates the latest innovations in testing, including techniques to test modern types of software such as OO, web applications, and embedded software.
1,079 citations
TL;DR: The author describes the Boolean satisfiability method for generating test patterns for single stuck-at faults in combinational circuits, which allows for the addition of heuristics used by structural search methods, and has produced excellent results on popular test pattern generation benchmarks.
Abstract: The author describes the Boolean satisfiability method for generating test patterns for single stuck-at faults in combinational circuits. This new method generates test patterns in two steps: first, it constructs a formula expressing the Boolean difference between the unfaulted and faulted circuits, and second, it applies a Boolean satisfiability algorithm to the resulting formula. This approach differs from previous methods now in use, which search the circuit structure directly instead of constructing a formula from it. The new method is general and effective. It allows for the addition of heuristics used by structural search methods, and it has produced excellent results on popular test pattern generation benchmarks. >
704 citations
TL;DR: This tutorial/survey paper will review the historical developments in this field, both in circuit realizations and in methods of handling multiple-valued design data, and consider the present state-of-the-art and future expectations.
Abstract: Multiple-valued logic, in which the number of discrete logic levels is not confined to two, has been the subject of much research over many years. The practical objective of this work has been to increase the information content of the digital signals in a system to a higher value than that provided by binary operation. In this tutorial/survey paper we will review the historical developments in this field, both in circuit realizations and in methods of handling multiple-valued design data, and consider the present state-of-the-art and future expectations.
489 citations
01 Apr 1997
TL;DR: It is demonstrated that binary decision diagrams are an efficient representation for every special-case matrix in common use, notably sparse matrices, and that complete pivoting is no more difficult over these matrices than partial pivoting.
Abstract: In this paper, we discuss the use of binary decision diagrams to represent general matrices. We demonstrate that binary decision diagrams are an efficient representation for every special-case matrix in common use, notably sparse matrices. In particular, we demonstrate that for any matrix, the BDD representation can be no larger than the corresponding sparse-matrix representation. Further, the BDD representation is often smaller than any other conventional special-case representation: for the n×n Walsh matrix, for example, the BDD representation is of size O(log n). No other special-case representation in common use represents this matrix in space less than O(n²). We describe termwise, row, column, block, and diagonal selection over these matrices, standard an Strassen matrix multiplication, and LU factorization. We demonstrate that the complexity of each of these operations over the BDD representation is no greater than that over any standard representation. Further, we demonstrate that complete pivoting is no more difficult over these matrices than partial pivoting. Finally, we consider an example, the Walsh Spectrum of a Boolean function.
432 citations
References
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01 Sep 1954
TL;DR: A class of multiple-error-correcting codes and their decoding scheme to device a coding scheme which is able to detect and correct such errors.
Abstract: linear error-correcting codes used in communications. (14) I. S. Reed, “A class of multiple-errorcorrecting codes and the decoding scheme,” IRE. Trans. A class of multiple-error-correcting codes and the decoding scheme. more. less. I. Reed · Details · Authors · Fields of science · Bibliography · Quotations · Similar. linear error correcting codes used in communications (2).For bit study is to device a coding scheme which is able to detect and correct such errors (6). (8) Reed, I. S., 'Class of multiple error correcting codes and their decoding scheme'.
868 citations
01 Sep 1954
TL;DR: It is shown that certain parts of the multiple output problem for switching circuits that have more than one output may be reduced to a single output problem whose inputs are equal in number to the sum of the numbers of inputs and outputs in the original problem.
Abstract: A solution is sought to the general problem of simplifying switching circuits that have more than one output. The mathematical treatment of the problem applies only to circuits that may be represented by “polynomials” in Boolean algebra. It is shown that certain parts of the multiple output problem for such circuits may be reduced to a single output problem whose inputs are equal in number to the sum of the numbers of inputs and outputs in the original problem. A particularly simple reduction may be effected in the case of two outputs. Various techniques are described for simplifying Boolean expressions, called “+ polynomials,” in which the operation “exclusive or” appears between terms. The methods described are particularly suitable for use with an automatic computer, and have been tested on the Illiac. An unexpected metric relationship is shown to exist between the members of certain classes of “+ polynomials” called “nets.” This relationship may be used for constructing error-detecting codes, provided the number of bits in the code is a power of two.
660 citations