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Opposition (boolean Algebra)
In Boolean algebra (logic), Boolean algebra, the consensus theorem or rule of consensus is the identity: :xy \vee \barz \vee yz = xy \vee \barz The consensus or resolvent of the terms xy and \barz is yz. It is the conjunction of all the unique literals of the terms, excluding the literal that appears unnegated in one term and negated in the other. If y includes a term that is negated in z (or vice versa), the consensus term yz is false; in other words, there is no consensus term. The conjunctive De Morgan's laws, dual of this equation is: :(x \vee y)(\bar \vee z)(y \vee z) = (x \vee y)(\bar \vee z) Proof : \begin xy \vee \barz \vee yz &= xy \vee \barz \vee (x \vee \bar)yz \\ &= xy \vee \barz \vee xyz \vee \baryz \\ &= (xy \vee xyz) \vee (\barz \vee \baryz) \\ &= xy(1\vee z)\vee\barz(1\vee y) \\ &= xy \vee \barz \end Consensus The consensus or consensus term of two conjunctive terms of a disjunction is de ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Karnaugh Map KV Race Hazard 10
Karnaugh is a surname. Notable people with the surname include: * Maurice Karnaugh (1924–2022), American physicist, mathematician, and inventor * Ron Karnaugh (born 1966), American retired swimmer See also * Karnaugh map {{surname ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Archie Blake (mathematician)
Charles Archibald Blake (November 24, 1906 - January 7, 1971), name officially changed to Archie Blake was an American mathematician. He is well known for the Blake canonical form, a normal form for expressions in propositional logic. In order to compute the canonical form, he moreover introduced the concept of consensus, which was a precursor of the resolution principle, today a common technique in automated theorem proving. Career In 1930, he became a member of the American Mathematical Society (AMS). He presented his canonical form at the AMS meeting at Columbia University on 29 Oct 1932. In 1937, this work lead to a Ph.D. from the University of Chicago, supervised by Raymond Walter Barnard. He worked for the United States Coast and Geodetic Survey in Washington, D.C., from 1936 (or earlier) as a mathematician, since 1938 as an Assistant Mathematician, and since 1939 as an Associated Mathematician. In 1946, he was appointed a Senior Statistician in the Office of the Arm ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Boolean Algebra
In mathematics and mathematical logic, Boolean algebra is a branch of algebra. It differs from elementary algebra in two ways. First, the values of the variable (mathematics), variables are the truth values ''true'' and ''false'', usually denoted by 1 and 0, whereas in elementary algebra the values of the variables are numbers. Second, Boolean algebra uses logical operators such as Logical conjunction, conjunction (''and'') denoted as , disjunction (''or'') denoted as , and negation (''not'') denoted as . Elementary algebra, on the other hand, uses arithmetic operators such as addition, multiplication, subtraction, and division. Boolean algebra is therefore a formal way of describing logical operations in the same way that elementary algebra describes numerical operations. Boolean algebra was introduced by George Boole in his first book ''The Mathematical Analysis of Logic'' (1847), and set forth more fully in his ''An Investigation of the Laws of Thought'' (1854). According to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
The Art Of Computer Programming
''The Art of Computer Programming'' (''TAOCP'') is a comprehensive multi-volume monograph written by the computer scientist Donald Knuth presenting programming algorithms and their analysis. it consists of published volumes 1, 2, 3, 4A, and 4B, with more expected to be released in the future. The Volumes 1–5 are intended to represent the central core of computer programming for sequential machines; the subjects of Volumes 6 and 7 are important but more specialized. When Knuth began the project in 1962, he originally conceived of it as a single book with twelve chapters. The first three volumes of what was then expected to be a seven-volume set were published in 1968, 1969, and 1973. Work began in earnest on Volume 4 in 1973, but was suspended in 1977 for work on typesetting prompted by the second edition of Volume 2. Writing of the final copy of Volume 4A began in longhand in 2001, and the first online pre-fascicle, 2A, appeared later in 2001. The first published installment ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Donald Ervin Knuth
Donald Ervin Knuth ( ; born January 10, 1938) is an American computer scientist and mathematician. He is a professor emeritus at Stanford University. He is the 1974 recipient of the Acm Turing award, ACM Turing Award, informally considered the Nobel Prize of computer science. Knuth has been called the "father of the analysis of algorithms". Knuth is the author of the multi-volume work ''The Art of Computer Programming''. He contributed to the development of the rigorous analysis of the computational complexity of algorithms and systematized formal mathematical techniques for it. In the process, he also popularized the Big O notation, asymptotic notation. In addition to fundamental contributions in several branches of theoretical computer science, Knuth is the creator of the TeX computer typesetting system, the related METAFONT font definition language and rendering system, and the Computer Modern family of typefaces. As a writer and scholar, Knuth created the WEB and CWEB compute ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Journal Of The ACM
The ''Journal of the ACM'' (''JACM'') is a peer-reviewed scientific journal covering computer science in general, especially theoretical aspects. It is an official journal of the Association for Computing Machinery. Its current editor-in-chief is Venkatesan Guruswami. The journal was established in 1954 and "computer scientists universally hold the ''Journal of the ACM'' in high esteem". See also * ''Communications of the ACM ''Communications of the ACM'' (''CACM'') is the monthly journal of the Association for Computing Machinery (ACM). History It was established in 1958, with Saul Rosen as its first managing editor. It is sent to all ACM members. Articles are i ...'' References External links * {{DEFAULTSORT:Journal Of The Acm Academic journals established in 1954 Computer science journals Association for Computing Machinery academic journals Bimonthly journals English-language journals ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Alan Robinson
John Alan Robinson (9 March 1930 – 5 August 2016) was a philosopher, mathematician, and computer scientist. He was a professor emeritus at Syracuse University. Alan Robinson's major contribution is to the foundations of automated theorem proving. His unification algorithm eliminated one source of combinatorial explosion in resolution provers; it also prepared the ground for the logic programming paradigm, in particular for the Prolog language. Robinson received the 1996 Herbrand Award for Distinguished Contributions to Automated Reasoning. Life Robinson was born in Halifax, Yorkshire, England in 1930 and left for the United States in 1952 with a classics degree from Cambridge University. He studied philosophy at the University of Oregon before moving to Princeton University where he received his PhD in philosophy in 1956. He then worked at DuPont as an operations research analyst, where he learned computer programming and taught himself mathematics. He moved to Rice U ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Willard Van Orman Quine
Willard Van Orman Quine ( ; known to his friends as "Van"; June 25, 1908 – December 25, 2000) was an American philosopher and logician in the analytic tradition, recognized as "one of the most influential philosophers of the twentieth century". He was the Edgar Pierce Chair of Philosophy at Harvard University from 1956 to 1978. Quine was a teacher of logic and set theory. He was famous for his position that first-order logic is the only kind worthy of the name, and developed his own system of mathematics and set theory, known as New Foundations. In the philosophy of mathematics, he and his Harvard colleague Hilary Putnam developed the Quine–Putnam indispensability argument, an argument for the Philosophy of mathematics#Empiricism, reality of mathematical entities.Colyvan, Mark"Indispensability Arguments in the Philosophy of Mathematics" The Stanford Encyclopedia of Philosophy (Fall 2004 Edition), Edward N. Zalta (ed.). He was the main proponent of the view that philosophy is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
The Journal Of Symbolic Logic
''The'' is a grammatical article in English, denoting nouns that are already or about to be mentioned, under discussion, implied or otherwise presumed familiar to listeners, readers, or speakers. It is the definite article in English. ''The'' is the most frequently used word in the English language; studies and analyses of texts have found it to account for seven percent of all printed English-language words. It is derived from gendered articles in Old English which combined in Middle English and now has a single form used with nouns of any gender. The word can be used with both singular and plural nouns, and with a noun that starts with any letter. This is different from many other languages, which have different forms of the definite article for different genders or numbers. Pronunciation In most dialects, "the" is pronounced as (with the voiced dental fricative followed by a schwa) when followed by a consonant sound, and as (homophone of the archaic pronoun ''thee' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Race Hazard
A race condition or race hazard is the condition of an electronics, software, or other system where the system's substantive behavior is dependent on the sequence or timing of other uncontrollable events, leading to unexpected or inconsistent results. It becomes a bug when one or more of the possible behaviors is undesirable. The term ''race condition'' was already in use by 1954, for example in David A. Huffman's doctoral thesis "The synthesis of sequential switching circuits". Race conditions can occur especially in logic circuits or multithreaded or distributed software programs. Using mutual exclusion can prevent race conditions in distributed software systems. In electronics A typical example of a race condition may occur when a logic gate combines signals that have traveled along different paths from the same source. The inputs to the gate can change at slightly different times in response to a change in the source signal. The output may, for a brief period, change t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Boolean Algebra (logic)
In mathematics and mathematical logic, Boolean algebra is a branch of algebra. It differs from elementary algebra in two ways. First, the values of the variable (mathematics), variables are the truth values ''true'' and ''false'', usually denoted by 1 and 0, whereas in elementary algebra the values of the variables are numbers. Second, Boolean algebra uses logical operators such as Logical conjunction, conjunction (''and'') denoted as , disjunction (''or'') denoted as , and negation (''not'') denoted as . Elementary algebra, on the other hand, uses arithmetic operators such as addition, multiplication, subtraction, and division. Boolean algebra is therefore a formal way of describing logical operations in the same way that elementary algebra describes numerical operations. Boolean algebra was introduced by George Boole in his first book ''The Mathematical Analysis of Logic'' (1847), and set forth more fully in his ''An Investigation of the Laws of Thought'' (1854). According to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Digital Logic
A logic gate is a device that performs a Boolean function, a logical operation performed on one or more binary inputs that produces a single binary output. Depending on the context, the term may refer to an ideal logic gate, one that has, for instance, zero rise time and unlimited fan-out, or it may refer to a non-ideal physical device (see ideal and real op-amps for comparison). The primary way of building logic gates uses diodes or transistors acting as electronic switches. Today, most logic gates are made from MOSFETs (metal–oxide–semiconductor field-effect transistors). ''From Integrated circuit'' They can also be constructed using vacuum tubes, electromagnetic relays with relay logic, fluidic logic, pneumatic logic, optics, molecules, acoustics, or even mechanical or thermal elements. Logic gates can be cascaded in the same way that Boolean functions can be composed, allowing the construction of a physical model of all of Boolean logic, and therefore, all of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
