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Boris Trakhtenbrot
Boris (Boaz) Abramovich Trakhtenbrot (russian: Борис Авраамович Трахтенброт, he, בועז טרכטנברוט; 19 February 1921 – 19 September 2016) was a Russian-Israeli mathematician in logic, algorithms, theory of computation, and cybernetics. Biography Trakhtenbrot was born 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 ... [...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 . People * (born in Briceva) * |
Theoretical Computer Science
Theoretical computer science (TCS) is a subset of general computer science and mathematics that focuses on mathematical aspects of computer science such as the theory of computation, lambda calculus, and type theory. It is difficult to circumscribe the theoretical areas precisely. The Association for Computing Machinery, ACM's ACM SIGACT, 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 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 n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1921 Births
Nineteen or 19 may refer to: * 19 (number), the natural number following 18 and preceding 20 * one of the years 19 BC, AD 19, 1919, 2019 Films * 19 (film), ''19'' (film), a 2001 Japanese film * Nineteen (film), ''Nineteen'' (film), a 1987 science fiction film Music * 19 (band), a Japanese pop music duo Albums * 19 (Adele album), ''19'' (Adele album), 2008 * ''19'', a 2003 album by Alsou * ''19'', a 2006 album by Evan Yo * ''19'', a 2018 album by MHD (rapper), MHD * ''19'', one half of the double album ''63/19'' by Kool A.D. * ''Number Nineteen'', a 1971 album by American jazz pianist Mal Waldron * XIX (EP), ''XIX'' (EP), a 2019 EP by 1the9 Songs * 19 (song), "19" (song), a 1985 song by British musician Paul Hardcastle. * "Nineteen", a song by Bad4Good from the 1992 album ''Refugee (Bad4Good album), Refugee'' * "Nineteen", a song by Karma to Burn from the 2001 album ''Almost Heathen''. * Nineteen (song), "Nineteen" (song), a 2007 song by American singer Billy Ray Cyrus ... [...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 ''Electronic Workshops in Computing'' (eWiC) is a publication series by the British Computer Society. The series provides free online access for conferences and workshops in the area of computing. For example, the EVA London Conference proceeding ...'', published by the British Computer Society References External links * Publications established in 1973 Computer science books Series of non-fiction books Springer ... [...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, claiming 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" informally refers collectively to the academic ranks of assistant professor, associate professor, or professor. This usage differs from the predominant usage of the word professor internationally, where the unqualified word professor only refers to "full professors." The majority of university lecturers and instructors in the United States, , do not occupy these tenure-track ranks, but are part-time adjuncts, or more commonly referred as college teachers. Research and education are among the main tasks of tenured and tenure-track professors, with the amount of time spent on research or teaching depending strongly on the type of institution. Publication of articles in conferences, journals, and books is essential to occupational advancement. As of August 2007, teaching in tertiary educational institutions is one of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Exact Science
The exact 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 Descartes, Leibniz, and 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 the "more natural of the branches of mathematics." ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Israel
Israel (; he, יִשְׂרָאֵל, ; ar, إِسْرَائِيل, ), officially the State of Israel ( he, מְדִינַת יִשְׂרָאֵל, label=none, translit=Medīnat Yīsrāʾēl; ), is a country in Western Asia. It is situated on the southeastern shore of the Mediterranean Sea and the northern shore of the Red Sea, and shares borders with Lebanon to the north, Syria to the northeast, Jordan to the east, and Egypt to the southwest. Israel also is bordered by the Palestinian territories of the West Bank and the Gaza Strip to the east and west, respectively. Tel Aviv is the economic and technological center of the country, while its seat of government is in its proclaimed capital of Jerusalem, although Israeli sovereignty over East Jerusalem is unrecognized internationally. The land held by present-day Israel witnessed some of the earliest human occupations outside Africa and was among the earliest known sites of agriculture. It was inhabited by the Canaanites ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Proceedings Of The USSR Academy Of Sciences
The ''Proceedings of the USSR Academy of Sciences'' (russian: Доклады Академии Наук СССР, ''Doklady Akademii Nauk SSSR'' (''DAN SSSR''), french: Comptes Rendus de l'Académie des Sciences de l'URSS) 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'' (russian: Доклады Академии Наук), 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. History The Russian Academy of Sciences dates from 1724, with a continuous series of variously named publications dat ... [...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". Mathematical formulation We follow the formulations as in Ebbinghaus and Flum Theorem : Satisfiability for finite structures is not decidable in first-order logic. :That is, the set is undecidable. Corollary Let σ be a relational vocabulary with one at least bi ... [...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 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 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 subrecursive hierarchies, formal methods, and formal languages. I ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Model Theory
In mathematical logic, model theory is the study of the relationship between formal theories (a collection of sentences in a formal language expressing statements about a mathematical structure), and their models (those 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 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 Shelah's stability theory. Compared to other areas of mathematical logic such as proof theory, model theory is often less concerned with formal rigour and closer in spirit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
