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Ehrenfeucht
Andrzej Ehrenfeucht (, born 8 August 1932) is a Polish-American mathematician and computer scientist. Life Andrzej Ehrenfeucht formulated the Ehrenfeucht–Fraïssé game, using the back-and-forth method given in Roland Fraïssé's PhD thesis. Also named for Ehrenfeucht is the Ehrenfeucht–Mycielski sequence. In 1971 Ehrenfeucht was a founding member of the Department of Computer Science at the University of Colorado at Boulder. He currently teaches and does research at the University, where he runs a project, "breaking away", with Patricia Baggett; the project, using hands-on activities, aims at raising high-school students' interest in mathematics and technology. Two of Ehrenfeucht's students, Eugene Myers and David Haussler, contributed to the sequencing of the human genome. They, with Harold Gabow, Ross McConnell, and Grzegorz Rozenberg, spoke at a 2012 University of Colorado two-day symposium honoring Ehrenfeucht's 80th birthday. Two journal issues have come out in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ehrenfeucht–Fraïssé Game
In the mathematical discipline of model theory, the Ehrenfeucht–Fraïssé game (also called back-and-forth games) is a technique based on game semantics for determining whether two structures are elementarily equivalent. The main application of Ehrenfeucht–Fraïssé games is in proving the inexpressibility of certain properties in first-order logic. Indeed, Ehrenfeucht–Fraïssé games provide a complete methodology for proving inexpressibility results for first-order logic. In this role, these games are of particular importance in finite model theory and its applications in computer science (specifically computer aided verification and database theory), since Ehrenfeucht–Fraïssé games are one of the few techniques from model theory that remain valid in the context of finite models. Other widely used techniques for proving inexpressibility results, such as the compactness theorem, do not work in finite models. Ehrenfeucht–Fraïssé-like games can also be defined for othe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ehrenfeucht–Mycielski Sequence
The Ehrenfeucht–Mycielski sequence is a recursively defined sequence of binary digits with pseudorandom properties, defined by . Definition The sequence starts with the single bit 0; each successive digit is formed by finding the longest suffix of the sequence that also occurs earlier within the sequence, and complementing the bit following the most recent earlier occurrence of that suffix. (The empty string is a suffix and prefix of every string.) For example, the first few steps of this construction process are: #0: initial bit #01: the suffix "" of "0" occurs earlier, most-recently followed by a 0, so add 1 #010: the suffix "" of "01" occurs earlier, most-recently followed by a 1, so add 0 #0100: the suffix "0" of "010" occurs earlier, most-recently followed by a 1, so add 0 #01001: the suffix "0" of "0100" occurs earlier, most-recently followed by a 0, so add 1 #010011: the suffix "01" of "01001" occurs earlier, most-recently followed by a 0, so add 1 #0100110: the suffix "1 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Roland Fraïssé
Roland Fraïssé (; 12 March 1920 – 30 March 2008) was a French mathematical logician. Fraïssé received his doctoral degree from the University of Paris in 1953. In his thesis, Fraïssé used the back-and-forth method to determine whether two model-theoretic structures were elementarily equivalent. This method of determining elementary equivalence was later formulated as the Ehrenfeucht–Fraïssé game. Fraïssé worked primarily in relation theory. Another of his important works was the Fraïssé construction of a Fraïssé limit of finite structures. He also formulated Fraïssé's conjecture on order embeddings, and introduced the notion of compensor in the theory of posets.Petits posets : dénombrement, représentabilité par cercles et compenseurs, Roland Fraïssé and Nik Lygeros, ''Comptes Rendus de l'Académie des Sciences'', Série I 313 (1991), no. 7, 417–420 Most of his career was spent as Professor at the University of Provence in Marseille Marseille ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Andrzej Mostowski
Andrzej Mostowski (1 November 1913 – 22 August 1975) was a Polish mathematician. He is perhaps best remembered for the Mostowski collapse lemma. Biography Born in Lemberg, Austria-Hungary, Mostowski entered University of Warsaw in 1931. He was influenced by Kuratowski, Lindenbaum, and Tarski. His Ph.D. came in 1939, officially directed by Kuratowski but in practice directed by Tarski who was a young lecturer at that time. He became an accountant after the German invasion of Poland but continued working in the Underground Warsaw University. After the Warsaw uprising of 1944, the Nazis tried to put him in a concentration camp. With the help of some Polish nurses, he escaped to a hospital, choosing to take bread with him rather than his notebook containing his research. Some of this research he reconstructed after the War, however much of it remained lost. His work was largely on recursion theory and undecidability. From 1946 until his death in Vancouver, British Columbia, Ca ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
David Haussler
David Haussler (born 1953) is an American bioinformatician known for his work leading the team that assembled the first human genome sequence in the race to complete the Human Genome Project and subsequently for comparative genome analysis that deepens understanding the molecular function and evolution of the genome. Haussler was elected a member of the National Academy of Engineering in 2018 for developments in computational learning theory and bioinformatics, including first assembly of the human genome, its analysis, and data sharing. He is a distinguished professor of biomolecular engineering and founding scientific director of the UC Santa Cruz Genomics Institute at the University of California, Santa Cruz, director of the California Institute for Quantitative Biosciences (QB3) on the UC Santa Cruz campus, and a consulting professor at the Stanford University School of Medicine and the UC San Francisco Biopharmaceutical Sciences Department. Education Haussler studied art ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cantor's Back-and-forth Method
In mathematical logic, especially set theory and model theory, the back-and-forth method is a method for showing isomorphism between countably infinite structures satisfying specified conditions. In particular it can be used to prove that * any two countably infinite densely ordered sets (i.e., linearly ordered in such a way that between any two members there is another) without endpoints are isomorphic. An isomorphism between linear orders is simply a strictly increasing bijection. This result implies, for example, that there exists a strictly increasing bijection between the set of all rational numbers and the set of all real algebraic numbers. * any two countably infinite atomless Boolean algebras are isomorphic to each other. * any two equivalent countable atomic models of a theory are isomorphic. * the Erdős–Rényi model of random graphs, when applied to countably infinite graphs, almost surely produces a unique graph, the Rado graph. * any two many-complete recursive ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jan Mycielski
Jan Mycielski (born February 7, 1932 in Wiśniowa, Podkarpackie Voivodeship, Poland)Curriculum vitae from Mycielski's web site, retrieved 2010-03-10. is a -American , a professor emeritus of mathematics at the . Academic career Mycielski received his Ph.D. in mathematics from the |
List Of Polish People
This is a partial list of notable Polish or Polish-speaking or -writing people. People of partial Polish heritage have their respective ancestries credited. Science Physics * Czesław Białobrzeski * Andrzej Buras * Georges Charpak, 1995 Nobel Prize * Jan Kazimierz Danysz * Marian Danysz * Tomasz Dietl * Maria Dworzecka * Artur Ekert, one of the independent inventors (in 1991) of quantum cryptography * Marek Gazdzicki * Ryszard Horodecki * Leopold Infeld * Aleksander Jabłoński * Jerzy Stanisław Janicki * Sylwester Kaliski * Elżbieta Kossecka * Jan Eugeniusz Krysiński * Stanislas Leibler * Maciej Lewenstein * Olga Malinkiewicz * Albert A. Michelson, 1907 Nobel Prize * Lidia Morawska * Stanisław Mrozowski * Władysław Natanson * Witold Nazarewicz * Henryk Niewodniczański * Georges Nomarski * Karol Olszewski * Jerzy Plebański * Jerzy Pniewski * Nikodem Popławski * Sylwester Porowski, blue laser * Józef Rotblat, 1995 Nobel Peace Prize * Stefan Rozental * ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alfred Tarski
Alfred Tarski (, born Alfred Teitelbaum;School of Mathematics and Statistics, University of St Andrews ''School of Mathematics and Statistics, University of St Andrews''. January 14, 1901 – October 26, 1983) was a Polish-American logician and mathematician. A prolific author best known for his work on model theory, metamathematics, and algebraic logic, he also contributed to abstract algebra, topology, geometry, measure theory, mathematical logic, set theory, and analytic philosophy. Educated in Poland at the University of Warsaw, and a member of the Lwów–Warsaw school of logic and the Warsaw school of mathematics, he immigrated to the United States in 1939 where he became a naturalized citizen in 1945. Tarski taught and carried out research in mathematics at the University of California, Berkeley, from 1942 until his death in 1983. Feferman A. His biographers Anita Burdman Feferman and Solomon Feferman state that, "Along with his contemporary, Kurt Gödel, he cha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Eugene Myers
Eugene Wimberly "Gene" Myers, Jr. (born December 31, 1953) is an American computer scientist and bioinformatician, who is best known for contributing to the early development of the NCBI's BLAST tool for sequence analysis. Education Myers received his Bachelor of Science in mathematics from the California Institute of Technology and a Doctor of Philosophy in computer science from the University of Colorado. Research Myers' 1990 paper (with Stephen Altschul and others) describing BLAST has received over 62,000+ citations making it amongst the most highly cited papers ever. Along with Udi Manber, Myers invented the suffix array data structure. Myers was a member of the faculty of the University of Arizona, the Vice President of Informatics Research at Celera Genomics, and a member of the faculty at UC Berkeley. At Celera Genomics, Myers was involved in the sequencing of the human genome, as well as the genomes of ''Drosophila'' and mouse. In particular, Myers advocated the use ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Living People
Related categories * :Year of birth missing (living people) / :Year of birth unknown * :Date of birth missing (living people) / :Date of birth unknown * :Place of birth missing (living people) / :Place of birth unknown * :Year of death missing / :Year of death unknown * :Date of death missing / :Date of death unknown * :Place of death missing / :Place of death unknown * :Missing middle or first names See also * :Dead people * :Template:L, which generates this category or death years, and birth year and sort keys. : {{DEFAULTSORT:Living people 21st-century people People by status ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Solomon Feferman
Solomon Feferman (December 13, 1928 – July 26, 2016) was an American philosopher and mathematician who worked in mathematical logic. Life Solomon Feferman was born in The Bronx in New York City to working-class parents who had immigrated to the United States after World War I and had met and married in New York. Neither parent had any advanced education. The family moved to Los Angeles, where Feferman graduated from high school at age 16. He received his B.S. from the California Institute of Technology in 1948, and in 1957 his Ph.D. in mathematics from the University of California, Berkeley, under Alfred Tarski, after having been drafted and having served in the U.S. Army from 1953 to 1955. In 1956 he was appointed to the Departments of Mathematics and Philosophy at Stanford University, where he later became the Patrick Suppes Professor of Humanities and Sciences. Feferman died on 26 July 2016 at his home in Stanford, following an illness that lasted three months and a stroke ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
