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Quine–McCluskey Algorithm
The Quine–McCluskey algorithm (QMC), also known as the method of prime implicants, is a method used for minimization of Boolean functions that was developed by Willard V. Quine in 1952 and extended by Edward J. McCluskey in 1956. As a general principle this approach had already been demonstrated by the logician Hugh McColl in 1878, was proved by Archie Blake in 1937, and was rediscovered by Edward W. Samson and Burton E. Mills in 1954 and by Raymond J. Nelson in 1955. Also in 1955, Paul W. Abrahams and John G. Nordahl as well as Albert A. Mullin and Wayne G. Kellner proposed a decimal variant of the method. The Quine–McCluskey algorithm is functionally identical to Karnaugh mapping, but the tabular form makes it more efficient for use in computer algorithms, and it also gives a deterministic way to check that the minimal form of a Boolean function has been reached. It is sometimes referred to as the tabulation method. The method involves two steps: # Finding all prime i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
NP-hard
In computational complexity theory, NP-hardness ( non-deterministic polynomial-time hardness) is the defining property of a class of problems that are informally "at least as hard as the hardest problems in NP". A simple example of an NP-hard problem is the subset sum problem. A more precise specification is: a problem ''H'' is NP-hard when every problem ''L'' in NP can be reduced in polynomial time to ''H''; that is, assuming a solution for ''H'' takes 1 unit time, ''H''s solution can be used to solve ''L'' in polynomial time. As a consequence, finding a polynomial time algorithm to solve any NP-hard problem would give polynomial time algorithms for all the problems in NP. As it is suspected that P≠NP, it is unlikely that such an algorithm exists. It is suspected that there are no polynomial-time algorithms for NP-hard problems, but that has not been proven. Moreover, the class P, in which all problems can be solved in polynomial time, is contained in the NP class. Defi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Journal Of Computer And System Sciences
The ''Journal of Computer and System Sciences'' (JCSS) is a peer-reviewed scientific journal in the field of computer science. ''JCSS'' is published by Elsevier, and it was started in 1967. Many influential scientific articles have been published in ''JCSS''; these include five papers that have won the Gödel Prize. an 2014 Gödel Prize Its managing editor is |
IEEE Transactions On Computer-Aided Design Of Integrated Circuits And Systems
''IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems'' (sometimes abbreviated ''IEEE TCAD'' or ''IEEE Transactions on CAD'') is a monthly peer-reviewed scientific journal covering the design, analysis, and use of computer-aided design of integrated circuits and systems. It is published by the IEEE Circuits and Systems Society and the IEEE Council on Electronic Design Automation (Institute of Electrical and Electronics Engineers). The journal was established in 1982 and the editor-in-chief is Rajesh K. Gupta (University of California at San Diego). According to the ''Journal Citation Reports'', the journal has a 2020 impact factor of 2.807. Past editor-in-chief * Rajesh K. Gupta (2018-2022) * Vijaykrishnan Narayanan (2014-2018) * Sachin Sapatnekar (2010-2014) See also *Electronic design automation Electronic design automation (EDA), also referred to as electronic computer-aided design (ECAD), is a category of software tools for designing Electron ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logic Friday
The ESPRESSO logic minimizer is a computer program using heuristic and specific algorithms for efficiently reducing the complexity of digital logic gate circuits. ESPRESSO-I was originally developed at IBM by Robert K. Brayton et al. in 1982. and improved as ESPRESSO-II in 1984. Richard L. Rudell later published the variant ESPRESSO-MV in 1986 and ESPRESSO-EXACT in 1987. Espresso has inspired many derivatives. Introduction Electronic devices are composed of numerous blocks of digital circuits, the combination of which performs the required task. The efficient implementation of logic functions in the form of logic gate circuits (such that no more logic gates are used than are necessary) is necessary to minimize production costs, and/or maximize a device's performance. Designing digital logic circuits All digital systems are composed of two elementary functions: memory elements for storing information, and combinational circuits that transform that information. State machin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Prentice Hall
Prentice Hall was an American major educational publisher owned by Savvas Learning Company. Prentice Hall publishes print and digital content for the 6–12 and higher-education market, and distributes its technical titles through the Safari Books Online e-reference service. History On October 13, 1913, law professor Charles Gerstenberg and his student Richard Ettinger founded Prentice Hall. Gerstenberg and Ettinger took their mothers' maiden names, Prentice and Hall, to name their new company. Prentice Hall became known as a publisher of trade books by authors such as Norman Vincent Peale; elementary, secondary, and college textbooks; loose-leaf information services; and professional books. Prentice Hall acquired the training provider Deltak in 1979. Prentice Hall was acquired by Gulf+Western in 1984, and became part of that company's publishing division Simon & Schuster. S&S sold several Prentice Hall subsidiaries: Deltak and Resource Systems were sold to National Education ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bell System Technical Journal
The ''Bell Labs Technical Journal'' is the in-house scientific journal for scientists of Nokia Bell Labs, published yearly by the IEEE society. The managing editor is Charles Bahr. The journal was originally established as the ''Bell System Technical Journal'' (BSTJ) in New York by the American Telephone and Telegraph Company (AT&T) in 1922, published under this name until 1983, when the breakup of the Bell System placed various parts of the system into separate companies. The journal was devoted to the scientific fields and engineering disciplines practiced in the Bell System for improvements in the wide field of electrical communication. After the restructuring of Bell Labs in 1984, the journal was renamed to ''AT&T Bell Laboratories Technical Journal''. In 1985, it was published as the ''AT&T Technical Journal'' until 1996, when it was renamed to ''Bell Labs Technical Journal''. History The ''Bell System Technical Journal'' was published by AT&T in New York City through its I ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
The American Mathematical Monthly
''The American Mathematical Monthly'' is a mathematical journal founded by Benjamin Finkel in 1894. It is published ten times each year by Taylor & Francis for the Mathematical Association of America. The ''American Mathematical Monthly'' is an expository journal intended for a wide audience of mathematicians, from undergraduate students to research professionals. Articles are chosen on the basis of their broad interest and reviewed and edited for quality of exposition as well as content. In this the ''American Mathematical Monthly'' fulfills a different role from that of typical mathematical research journals. The ''American Mathematical Monthly'' is the most widely read mathematics journal in the world according to records on JSTOR. Tables of contents with article abstracts from 1997–2010 are availablonline The MAA gives the Lester R. Ford Awards annually to "authors of articles of expository excellence" published in the ''American Mathematical Monthly''. Editors *2022– ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Qualitative Comparative Analysis
In statistics, qualitative comparative analysis (QCA) is a data analysis based on set theory to examine the relationship of conditions to outcome. QCA describes the relationship in terms of necessary conditions and sufficient conditions. The technique was originally developed by Charles Ragin in 1987 to study data sets that are too small for linear regression analysis but large for cross-case analysis. Summary of technique In the case of categorical variables, QCA begins by listing and counting all types of cases which occur, where each type of case is defined by its unique combination of values of its independent and dependent variables. For instance, if there were four categorical variables of interest, , and A and B were dichotomous (could take on two values), C could take on five values, and D could take on three, then there would be 60 possible types of observations determined by the possible combinations of variables, not all of which would necessarily occur in real life. B ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Buchberger's Algorithm
In the theory of multivariate polynomials, Buchberger's algorithm is a method for transforming a given set of polynomials into a Gröbner basis, which is another set of polynomials that have the same common zeros and are more convenient for extracting information on these common zeros. It was introduced by Bruno Buchberger simultaneously with the definition of Gröbner bases. Euclidean algorithm for polynomial greatest common divisor computation and Gaussian elimination of linear systems are special cases of Buchberger's algorithm when the number of variables or the degrees of the polynomials are respectively equal to one. For other Gröbner basis algorithms, see . Algorithm A crude version of this algorithm to find a basis for an ideal of a polynomial ring ''R'' proceeds as follows: :Input A set of polynomials ''F'' that generates :Output A Gröbner basis ''G'' for :# ''G'' := ''F'' :# For every ''fi'', ''fj'' in ''G'', denote by ''gi'' the leading term of ''fi'' with resp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Blake Canonical Form
In Boolean logic, a formula for a Boolean function ''f'' is in Blake canonical form (BCF), also called the complete sum of prime implicants, the complete sum, or the disjunctive prime form, when it is a disjunction of all the prime implicants of ''f''. Relation to other forms The Blake canonical form is a special case of disjunctive normal form. The Blake canonical form is not necessarily minimal (upper diagram), however all the terms of a minimal sum are contained in the Blake canonical form. On the other hand, the Blake canonical form is a canonical form, that is, it is unique up to reordering, whereas there can be multiple minimal forms (lower diagram). Selecting a minimal sum from a Blake canonical form amounts in general to solving the set cover problem, so is NP-hard. History Archie Blake presented his canonical form at a meeting of the American Mathematical Society in 1932, and in his 1937 dissertation. He called it the "simplified canonical form"; it was named the "B ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Petrick's Method
In Boolean algebra, Petrick's method (also known as ''Petrick function'' or ''branch-and-bound'' method) is a technique described by Stanley R. Petrick (1931–2006) in 1956 for determining all minimum sum-of-products solutions from a prime implicant chart. Petrick's method is very tedious for large charts, but it is easy to implement on a computer. The method was improved by Insley B. Pyne and Edward Joseph McCluskey in 1962. Algorithm # Reduce the prime implicant chart by eliminating the essential prime implicant rows and the corresponding columns. # Label the rows of the reduced prime implicant chart P_1, P_2, P_3, P_4, etc. # Form a logical function P which is true when all the columns are covered. ''P'' consists of a product of sums where each sum term has the form (P_ + P_ + \cdots + P_), where each P_ represents a row covering column i. # Reduce P to a minimum sum of products by multiplying out and applying the absorption law In algebra, the absorption law or absorption ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
