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Schützenberger
Schützenberger may refer to these people: * Anne Ancelin Schützenberger (1919–2018) (de) * Paul Schützenberger, French chemist * René Schützenberger, French painter * Marcel-Paul "Marco" Schützenberger, French mathematician and Doctor of Medicine, known for # Schutzenberger group # Schützenberger theorem # Chomsky–Schützenberger enumeration theorem # Chomsky–Schützenberger representation theorem # Chomsky–Schützenberger hierarchy In formal language theory, computer science and linguistics, the Chomsky hierarchy (also referred to as the Chomsky–Schützenberger hierarchy) is a containment hierarchy of classes of formal grammars. This hierarchy of grammars was described by ... German-language surnames French families Alsatian-German people {{DEFAULTSORT:Schutzenberger ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Marcel-Paul Schützenberger
Marcel-Paul "Marco" Schützenberger (24 October 1920 – 29 July 1996) was a French mathematician and Doctor of Medicine. He worked in the fields of formal language, combinatorics, and information theory.Herbert Wilf, Dominique Foata, ''et al.'',In Memoriam: Marcel-Paul Schützenberger, 1920-1996," ''Electronic Journal of Combinatorics'', served from University of Pennsylvania Dept. of Mathematics Server, article dated 12 October 1996, retrieved from WWW on 4 November 2006. In addition to his formal results in mathematics, he was "deeply involved in struggle against the votaries of eo-arwinism",Foata, Dominique, "In Memoriam," ''op. cit.'' a stance which has resulted in some mixed reactions from his peers and from critics of his stance on evolution. Several notable theorems and objects in mathematics as well as computer science bear his name (for example Schutzenberger group or the Chomsky–Schützenberger hierarchy). Paul Schützenberger was his great-grandfather. In the lat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
René Schützenberger
René-Paul Schützenberger (29 July 1860 – 31 December 1916) was a French Post-Impressionist painter. Biography Born in Mulhouse, into an Alsatian family of famous brewers, he was the son of Paul Schützenberger (1829–1897), a French chemist. The painter Louis-Frédéric Schützenberger (1825–1903) was his cousin. René Schützenberger studied at the Académie Julian, a private art school founded by Rodolphe Julian under Jean-Paul Laurens. In 1891, he married Andrée-Marie Bouland in the town hall of the 6th arrondissement of Paris. She was a writer and an art critique known as Andrée Myra. Schützenberger started to exhibit at the Salon des Artistes Français in 1889, at the Salon des Indépendants from 1902 and at the Société Nationale des Beaux-Arts from 1907. He got an honourable mention at the Salon of 1897 and at the Universal Exhibition of 1900. In 1911, Schützenberger exhibited at the ''Exposition des Peintres du Paris moderne'' in the Gallery ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Anne Ancelin Schützenberger
Anne Ancelin Schützenberger (29 March 1919 – 23 March 2018) was a French psychologist and psychotherapist. During the Second World War she was a member of the French Resistance. She was born in Moscow, into a Jewish family, but grew up in Paris, where she received her education, leading eventually to doctorates in literature and psychology. As a result of her Resistance activities, she became regional secretary of the newly-formed Mouvement de libération nationale in 1944, and on 6 June of the same year her home was burned down by the 2nd SS Panzer Division Das Reich. Having gained experience working on the MLN's journal, in 1947 she launched the ''Bulletin de Psychologie des Étudiants de l'Université de Paris'', which she later edited, producing the first issue in the kitchen of her apartment. On 30 August 1948, she married the mathematician Marcel-Paul Schützenberger in London; they had one daughter, Hélène, but divorced soon afterwards. Through her husband she ca ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Paul Schützenberger
Paul Schützenberger (23 December 1829 – 26 June 1897) was a French chemist. He was born in Strasbourg, where his father Georges Frédéric Schützenberger (1779–1859) was professor of law, and his uncle Charles Schützenberger (1809–1881) professor of chemical medicine. He was intended for a medical career and graduated MD from the University of Strasbourg in 1855, but his interests laid in physical and chemical sciences. In 1853 he went to Paris as preparateur to JF Persoz (1805–1868), professor of chemistry at the Conservatoire des Arts et Métiers. A year later he was entrusted with a course of chemical instruction at Mulhouse, and he remained in that town until 1865 as professor at the École Supérieure des Sciences. He then returned to Paris as assistant to AJ Balard at the College de France, in 1876 he succeeded him in the chair of chemistry, and in 1882 he became directing professor at the municipal École de Physique et de Chimie. The two latter chairs he hel ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chomsky–Schützenberger Enumeration Theorem
In formal language theory, the Chomsky–Schützenberger enumeration theorem is a theorem derived by Noam Chomsky and Marcel-Paul Schützenberger about the number of words of a given length generated by an unambiguous context-free grammar. The theorem provides an unexpected link between the theory of formal languages and abstract algebra. Statement In order to state the theorem, a few notions from algebra and formal language theory are needed. Let \mathbb denote the set of nonnegative integers. A ''power series'' over \mathbb is an infinite series of the form :f = f(x) = \sum_^\infty a_k x^k = a_0 + a_1 x^1 + a_2 x^2 + a_3 x^3 + \cdots with coefficients a_k in \mathbb. The ''multiplication'' of two formal power series f and g is defined in the expected way as the convolution of the sequences a_n and b_n: :f(x)\cdot g(x) = \sum_^\infty \left(\sum_^k a_i b_\right) x^k. In particular, we write f^2 = f(x)\cdot f(x), f^3 = f(x)\cdot f(x)\cdot f(x), and so on. In analogy to algebra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Schützenberger Theorem
In mathematics, a factorisation of a free monoid is a sequence of subsets of words with the property that every word in the free monoid can be written as a concatenation of elements drawn from the subsets. The Chen–Fox–Lyndon theorem states that the Lyndon words furnish a factorisation. The Schützenberger theorem relates the definition in terms of a multiplicative property to an additive property. Let ''A''* be the free monoid on an alphabet ''A''. Let ''X''''i'' be a sequence of subsets of ''A''* indexed by a totally ordered index set ''I''. A factorisation of a word ''w'' in ''A''* is an expression :w = x_ x_ \cdots x_ \ with x_ \in X_ and i_1 \ge i_2 \ge \ldots \ge i_n. Some authors reverse the order of the inequalities. Chen–Fox–Lyndon theorem A Lyndon word over a totally ordered alphabet ''A'' is a word that is lexicographically less than all its rotations.Lothaire (1997) p.64 The Chen–Fox–Lyndon theorem states that every string may be formed in a unique w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chomsky–Schützenberger Representation Theorem
In formal language theory, the Chomsky–Schützenberger representation theorem is a theorem derived by Noam Chomsky and Marcel-Paul Schützenberger about representing a given context-free language in terms of two simpler languages. These two simpler languages, namely a regular language and a Dyck language, are combined by means of an intersection and a homomorphism. A few notions from formal language theory are in order. A context-free language is '' regular'', if it can be described by a regular expression, or, equivalently, if it is accepted by a finite automaton. A homomorphism is based on a function h which maps symbols from an alphabet \Gamma to words over another alphabet \Sigma; If the domain of this function is extended to words over \Gamma in the natural way, by letting h(xy)=h(x)h(y) for all words x and y, this yields a ''homomorphism'' h:\Gamma^*\to \Sigma^*. A ''matched alphabet'' T \cup \overline T is an alphabet with two equal-sized sets; it is convenient to think ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chomsky Hierarchy
In formal language theory, computer science and linguistics, the Chomsky hierarchy (also referred to as the Chomsky–Schützenberger hierarchy) is a containment hierarchy of classes of formal grammars. This hierarchy of grammars was described by Noam Chomsky in 1956. It is also named after Marcel-Paul Schützenberger, who played a crucial role in the development of the theory of formal languages. Formal grammars A formal grammar of this type consists of a finite set of '' production rules'' (''left-hand side'' → ''right-hand side''), where each side consists of a finite sequence of the following symbols: * a finite set of ''nonterminal symbols'' (indicating that some production rule can yet be applied) * a finite set of ''terminal symbols'' (indicating that no production rule can be applied) * a ''start symbol'' (a distinguished nonterminal symbol) A formal grammar provides an axiom schema for (or ''generates'') a ''formal language'', which is a (usually infinite) s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
German-language Surnames
German ( ) is a West Germanic language mainly spoken in Central Europe. It is the most widely spoken and official or co-official language in Germany, Austria, Switzerland, Liechtenstein, and the Italian province of South Tyrol. It is also a co-official language of Luxembourg and Belgium, as well as a national language in Namibia. Outside Germany, it is also spoken by German communities in France (Bas-Rhin), Czech Republic (North Bohemia), Poland (Upper Silesia), Slovakia (Bratislava Region), and Hungary (Sopron). German is most similar to other languages within the West Germanic language branch, including Afrikaans, Dutch, English, the Frisian languages, Low German, Luxembourgish, Scots, and Yiddish. It also contains close similarities in vocabulary to some languages in the North Germanic group, such as Danish, Norwegian, and Swedish. German is the second most widely spoken Germanic language after English, which is also a West Germanic language. German is one of the major ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
French Families
French (french: français(e), link=no) may refer to: * Something of, from, or related to France ** French language, which originated in France, and its various dialects and accents ** French people, a nation and ethnic group identified with France ** French cuisine, cooking traditions and practices Fortnite French places Arts and media * The French (band), a British rock band * "French" (episode), a live-action episode of ''The Super Mario Bros. Super Show!'' * ''Française'' (film), 2008 * French Stewart (born 1964), American actor Other uses * French (surname), a surname (including a list of people with the name) * French (tunic), a particular type of military jacket or tunic used in the Russian Empire and Soviet Union * French's, an American brand of mustard condiment * French catheter scale The French scale, French gauge or Charrière system is commonly used to measure the size of a catheter. It is most often abbreviated as Fr, but can often be seen abbreviated as Fg, FR ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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