|
Boris Trakhtenbrot
Boris (Boaz) Abramovich Trakhtenbrot (, ; 19 February 1921 – 19 September 2016) was a Russian-Israeli mathematician in logic, algorithms, theory of computation, and cybernetics. Biography Trakhtenbrot was born into a Jewish family in Brichevo, northern Bessarabia (now Tîrnova, Moldova). He studied at the Moldovan State Pedagogical Institute in Kishinev, Chernivtsi University, and the Ukrainian Academy of Science's Mathematical Institute, completing a Ph.D. at the latter institution in 1950. He worked at Akademgorodok, Novosibirsk during the 1960s and 1970s. In 1964 Trakhtenbrot discovered and proved a fundamental result in theoretical computer science called the gap theorem. He also discovered and proved the theorem in logic, model theory, and computability theory now known as Trakhtenbrot's theorem. After immigrating to Israel in 1981, he became a professor in the Faculty of Exact Sciences at Tel Aviv University, and continued as professor emeritus ''Emeritus/Eme ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tîrnova, Dondușeni
Tîrnova is a commune in Dondușeni District, Moldova. It is composed of three villages: Briceva, Elenovca (formerly ''Elena-Doamnă'') and Tîrnova. Briceva (also ''Brichevo'', ''Bricheva'', ) was established as a Jewish agricultural colony in 1836 and maintained Jewish majority until World War II. People * Gary Bertini (born in Briceva) * Boris Trakhtenbrot (born in Briceva) * Mihail ȘleahtițchiReferences External links [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Theoretical Computer Science
Theoretical computer science is a subfield of computer science and mathematics that focuses on the Abstraction, abstract and mathematical foundations of computation. It is difficult to circumscribe the theoretical areas precisely. The Association for Computing Machinery, ACM's Special Interest Group on Algorithms and Computation Theory (SIGACT) provides the following description: History While logical inference and mathematical proof had existed previously, in 1931 Kurt Gödel proved with his incompleteness theorem that there are fundamental limitations on what statements could be proved or disproved. Information theory was added to the field with A Mathematical Theory of Communication, a 1948 mathematical theory of communication by Claude Shannon. In the same decade, Donald Hebb introduced a mathematical model of Hebbian learning, learning in the brain. With mounting biological data supporting this hypothesis with some modification, the fields of neural networks and para ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1921 Births
Events January * January 2 ** The Association football club Cruzeiro Esporte Clube, from Belo Horizonte, is founded as the multi-sports club Palestra Italia by Italian expatriates in First Brazilian Republic, Brazil. ** The Spanish liner ''Santa Isabel'' breaks in two and sinks off Villa Garcia, Mexico, with the loss of 244 of the 300 people on board. * January 16 – The Marxist Left in Slovakia and the Transcarpathian Ukraine holds its founding congress in Ľubochňa. * January 17 – The first recorded public performance of the illusion of "sawing a woman in half" is given by English stage magician P. T. Selbit at the Finsbury Park Empire variety theatre in London. * January 20 – British K-class submarine HMS K5, HMS ''K5'' sinks in the English Channel; all 57 on board are lost. * January 21 – The full-length Silent film, silent comedy drama film ''The Kid (1921 film), The Kid'', written, produced, directed by and starring Charlie Chaplin (in his ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lecture Notes In Computer Science
''Lecture Notes in Computer Science'' is a series of computer science books published by Springer Science+Business Media since 1973. Overview The series contains proceedings, post-proceedings, monographs, and Festschrifts. In addition, tutorials, state-of-the-art surveys, and "hot topics" are increasingly being included. The series is indexed by DBLP. See also *'' Monographiae Biologicae'', another monograph series published by Springer Science+Business Media *'' Lecture Notes in Physics'' *'' Lecture Notes in Mathematics'' *'' Electronic Workshops in Computing'', published by the British Computer Society image:Maurice Vincent Wilkes 1980 (3).jpg, Sir Maurice Wilkes served as the first President of BCS in 1957. The British Computer Society (BCS), branded BCS, The Chartered Institute for IT, since 2009, is a professional body and a learned ... References External links * Academic journals established in 1973 Computer science books Series of non-fiction books ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Association For Computing Machinery
The Association for Computing Machinery (ACM) is a US-based international learned society for computing. It was founded in 1947 and is the world's largest scientific and educational computing society. The ACM is a non-profit professional membership group, reporting nearly 110,000 student and professional members . Its headquarters are in New York City. The ACM is an umbrella organization for academic and scholarly interests in computer science (informatics). Its motto is "Advancing Computing as a Science & Profession". History In 1947, a notice was sent to various people: On January 10, 1947, at the Symposium on Large-Scale Digital Calculating Machinery at the Harvard computation Laboratory, Professor Samuel H. Caldwell of Massachusetts Institute of Technology spoke of the need for an association of those interested in computing machinery, and of the need for communication between them. ..After making some inquiries during May and June, we believe there is ample interest to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Professors In The United States
Professors in the United States commonly occupy any of several positions of teaching and research within a college or university. In the U.S., the word "professor" is often used to refer to anyone who teaches at a college of university level at any academic rank. This usage differs from the predominant usage of the word professor in other countries, where the unqualified word "professor" only refers to "full professors" (i.e., the highest rank among regular faculty), nor is it generally used in the United States for secondary education teachers. Other tenure-track faculty positions include assistant professor (entry level) and associate professor (mid-level). Other teaching-focused positions that use the term "professor" include Clinical Professor, Professor of Practice, and Teaching Professor (specific roles and status vary widely among institutions, but usually do not involve tenure). Most faculty with titles of "Lecturer" and "Instructor" in the U.S. are not eligible for ten ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Exact Science
The exact sciences or quantitative sciences, sometimes called the exact mathematical sciences, are those sciences "which admit of absolute precision in their results"; especially the mathematical sciences. Examples of the exact sciences are mathematics, optics, astronomy, and physics, which many philosophers from René Descartes, Gottfried Leibniz, and Immanuel Kant to the logical positivists took as paradigms of rational and objective knowledge. These sciences have been practiced in many cultures from antiquity to modern times. Given their ties to mathematics, the exact sciences are characterized by accurate quantitative expression, precise predictions and/or rigorous methods of testing hypotheses involving quantifiable predictions and measurements. The distinction between the quantitative exact sciences and those sciences that deal with the causes of things is due to Aristotle, who distinguished mathematics from natural philosophy and considered the exact sciences to be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Israel
Israel, officially the State of Israel, is a country in West Asia. It Borders of Israel, shares borders with Lebanon to the north, Syria to the north-east, Jordan to the east, Egypt to the south-west, and the Mediterranean Sea to the west. Israeli-occupied territories, It occupies the Occupied Palestinian territories, Palestinian territories of the West Bank in the east and the Gaza Strip in the south-west. Israel also has a small coastline on the Red Sea at its southernmost point, and part of the Dead Sea lies along its eastern border. Status of Jerusalem, Its proclaimed capital is Jerusalem, while Tel Aviv is the country's Gush Dan, largest urban area and Economy of Israel, economic center. Israel is located in a region known as the Land of Israel, synonymous with the Palestine (region), Palestine region, the Holy Land, and Canaan. In antiquity, it was home to the Canaanite civilisation followed by the History of ancient Israel and Judah, kingdoms of Israel and Judah. Situate ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Proceedings Of The USSR Academy Of Sciences
The ''Proceedings of the USSR Academy of Sciences'' (, ''Doklady Akademii Nauk SSSR'' (''DAN SSSR''), ) was a Soviet journal that was dedicated to publishing original, academic research papers in physics, mathematics, chemistry, geology, and biology. It was first published in 1933 and ended in 1992 with volume 322, issue 3. Today, it is continued by ''Doklady Akademii Nauk'' (), which began publication in 1992. The journal is also known as the ''Proceedings of the Russian Academy of Sciences (RAS)''. ''Doklady'' has had a complicated publication and translation history. A number of translation journals exist which publish selected articles from the original by subject section; these are listed below. The journal is indexed in Russian Science Citation Index. History The Russian Academy of Sciences dates from 1724, with a continuous series of variously named publications dating from 1726. ''Doklady Akademii Nauk SSSR-Comptes Rendus de l'Académie des Sciences de l'URSS, Seriya ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Trakhtenbrot's Theorem
In logic, finite model theory, and computability theory, Trakhtenbrot's theorem (due to Boris Trakhtenbrot) states that the problem of validity in first-order logic on the class of all finite models is undecidable. In fact, the class of valid sentences over finite models is not recursively enumerable (though it is co-recursively enumerable). Trakhtenbrot's theorem implies that Gödel's completeness theorem (that is fundamental to first-order logic) does not hold in the finite case. Also it seems counter-intuitive that being valid over all structures is 'easier' than over just the finite ones. The theorem was first published in 1950: "The Impossibility of an Algorithm for the Decidability Problem on Finite Classes". The theorem is related to Church's result that the set of valid formulas in first-order logic is not decidable (however this set is semi-decidable). Mathematical formulation We follow the formulations as in Ebbinghaus and Flum. Theorem : Satisfiability for finit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computability Theory
Computability theory, also known as recursion theory, is a branch of mathematical logic, computer science, and the theory of computation that originated in the 1930s with the study of computable functions and Turing degrees. The field has since expanded to include the study of generalized computability and definable set, definability. In these areas, computability theory overlaps with proof theory and effective descriptive set theory. Basic questions addressed by computability theory include: * What does it mean for a function (mathematics), function on the natural numbers to be computable? * How can noncomputable functions be classified into a hierarchy based on their level of noncomputability? Although there is considerable overlap in terms of knowledge and methods, mathematical computability theorists study the theory of relative computability, reducibility notions, and degree structures; those in the computer science field focus on the theory of computational complexity theory ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Model Theory
In mathematical logic, model theory is the study of the relationship between theory (mathematical logic), formal theories (a collection of Sentence (mathematical logic), sentences in a formal language expressing statements about a Structure (mathematical logic), mathematical structure), and their Structure (mathematical logic), models (those Structure (mathematical logic), structures in which the statements of the theory hold). The aspects investigated include the number and size of models of a theory, the relationship of different models to each other, and their interaction with the formal language itself. In particular, model theorists also investigate the sets that can be definable set, defined in a model of a theory, and the relationship of such definable sets to each other. As a separate discipline, model theory goes back to Alfred Tarski, who first used the term "Theory of Models" in publication in 1954. Since the 1970s, the subject has been shaped decisively by Saharon Shel ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
