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	Manuel Blum - Wikipedia, the free encyclopedia
		Manuel Blum (born 26 April 1938 in Caracas, Venezuela) is a computer scientist who received the Turing Award in 1995 "In recognition of his contributions to the foundations of computational complexity theory and its application to cryptography and program checking".
		Blum attended MIT, where he received his bachelor's degree in 1959, his master's degree in 1961, and his Ph.D. in 1964 under professor Marvin Minsky.
		The theory is based on gödel numberings and the Blum axioms.
	en.wikipedia.org /wiki/Manuel_Blum (213 words)

	Encyclopedia: Lenore Blum
		Lenore Blum's research, from her early work in model theory and differential fields (logic and algebra) to her more recent work with Shub and Smale in developing a theory of computation and complexity over the real numbers (mathematics and computer science), has focused on merging seemingly unrelated areas.
		Blum is well known for her work in increasing the participation of girls and women in mathematics and scientific fields.
		Lenore is married to Manuel Blum and mother of Avrim Blum, both also MIT alumni and professors of Computer Science at Carnegie Mellon.
	www.nationmaster.com /encyclopedia/Lenore-Blum (1107 words)

	Carnegie Mellon Press Release: May 9, 2002
		Blum is one of the founders of computational complexity theory, work that has also had applications to cryptography and program checking.
		Blum attended the Massachusetts Institute of Technology where he received his bachelor's, and master's degrees in electrical engineering in 1959 and '61, and a doctor's degree in mathematics in 1964.
		Blum is one of 72 new members of the National Academy of Sciences chosen this year in recognition of their distinguished and continuing achievement in original research.
	www.cmu.edu /PR/releases02/020509_mblum.html (701 words)

	Search Encyclopedia.com
		Juan Manuel, Infante de Castile Juan Manuel, Infante de Castilehwän mänwĕl´, ēnfän´tā thā kästē´lā, 1282-1349?, Spanish nobleman, soldier, and writer; nephew of Alfonso X (called the Wise).
		Manuel Odría, Manuelmänooĕl´ ōdrē´ä, 1897-1974, president of Peru (1948-56).
		Roxas, Manuel Roxas, Manuelmänwĕl´ rō´häs, 1894-1948, Philippine statesman, b.
	www.encyclopedia.com /search.asp?target=Manuel+Blum&rc=10&fh=11&fr=11 (434 words)

	Dad, mom join son to form a potent computer science team at CMU
		Lenore, Avrim and Manuel Blum on the CMU campus.
		Manuel was five years older, but he became her "secret person," a confidant with whom she could discuss psychology, logic and a whole range of topics that her schoolmates couldn't comprehend.
		Manuel also became renowned as a mentor, both for a supportive, Socratic style that endeared him to his students, and for turning out students who almost uniformly have become leaders in the field.
	www.post-gazette.com /healthscience/20011021blum1021p3.asp (2100 words)

	Blum (Site not responding. Last check: 2007-09-06)
		We should make it clear from the beginning of this biography of Lenore Blum that Blum is her married name which she only took after marrying Manual Blum, who was also a mathematician.
		Blum's next important paper was Differentially closed fields: a model-theoretic tour which appeared in 1977 and, for the first time, made accessible some results she had found ten years earlier and included in her thesis.
		An important first contribution was Blum's 1989 paper Lectures on a theory of computation and complexity over the reals (or an arbitrary ring) which extended the theories of computation and computational complexity from the standard discrete situation to study how these ideas can be developed in continuous domains such as the real number system.
	www-history.mcs.st-and.ac.uk /history/Mathematicians/Blum.html (1622 words)

	Pinnacle 2002 – Masters’ Biographies
		Manuel Blum is Carnegie Mellon University's Bruce Nelson Professor of Computer Science and a member of the National Academy of Sciences.
		In the fall of 1999, Lenore and her husband Manuel had the good fortune to be able to join their son Avrim on the faculty of the School of Computer Science at Carnegie Mellon University.
		Blum is also well known for her work in increasing the participation of girls and women in mathematics and scientific fields.
	www.apa.org /ed/cgepmasters.html (2373 words)

	Lenore Blum
		Blum's research, from her early work in model theory and differential fields (logic and algebra) to her more recent work with Shub and Smale in developing a theory of computation and complexity over the real numbers (mathematics and computer science), has focused on merging seemingly unrelated areas.
		Blum is internationally recognized for her work in increasing the participation of girls and women in mathematics and scientific fields.
		She is married to Manuel Blum and mother of Avrim Blum, both also MIT alumni and professors of Computer Science at Carnegie Mellon.
	www.cs.columbia.edu /wics/lenore_blum.htm (610 words)

	Blum Julius Blum Gmbh - Herzlich Willkommen Blum. Blum Country Websites. Blum International Website (Site not responding. Last check: 2007-09-06)
		Johann Heinrich Blum (1752-1824) was born in Bethlehem PA. He left the Moravian church as a young man to join the Revolutionary forces, and narrowly escaped death.
		Blum Shapiro is an accounting, auditing, tax and business consulting firm in West Hartford, CT. With a staff of 140 people, Blum Shapiro is the largest regional CPA firm in Connecticut and firms in the U. Blum Shapiro offers accounting, auditing and tax services.
		Zevi Blum was born in Paris in 1933 In addition to etchings, Zevi Blum.
	www.99hosted.com /names5911.html (405 words)

	Search Encyclopedia.com
		Altamirano, Ignacio Manuel Altamirano, Ignacio Manuelēgnä´syō mänwĕl´ ältämērä´nō, 1834-93, Mexican novelist and poet.
		C?edes, Carlos Manuel de Céspedes, Carlos Manuel dekär´lōs mänwĕl´ dā sā´spāthās, 1819-74, Cuban revolutionist.
		Godoy, Manuel de Godoy, Manuel demänwĕl´ dā gōthoi´, 1767-1851, Spanish statesman.
	www.encyclopedia.com /search.asp?target=Manuel+Blum&rc=10&fh=7&fr=21 (488 words)

	CMU professor honored - PittsburghLIVE.com
		Manuel Blum is just as interested in deciphering what a computer can do as what it can't do.
		Blum's pioneering work in computers — the Carnegie Mellon University professor is now tackling a program to curb identity theft — has merited his election to the National Academy of Sciences, one of the nation's highest honors for a scientist or engineer.
		Blum taught at the University of California at Berkeley for 30 years before he and his wife, Lenore, also a computer science professor, came to CMU in 1999.
	www.pittsburghlive.com /x/search/s_71679.html (832 words)

	ACM'S A.M. Turing Award, computing's highest honor, goes to Manuel Blum of University of California, Berkeley (Site not responding. Last check: 2007-09-06)
		Blum shows that secure business transactions, pseudo-random number generation, and program checking are all possible precisely because all computational devices are resource bounded.
		Blum is one of the founders of computational complexity theory, a field that is central to theoretical computer science, and one which deals with measuring the difficulty of performing computations.
		Dr. Blum was born in Caracas, Venezuela in 1938 and began his academic career at the Massachusetts Institute of Technology, where he received his B.S., M.S., and Ph.D degrees.
	grail.cba.csuohio.edu /~mcintyre/cis490/95turing.htm (615 words)

	Professor tries to instill passion for math, science (Site not responding. Last check: 2007-09-06)
		Blum loves the challenge of working with young teens, many who use the computer only to exchange instant messages with their friends, she suspects.
		She eventually switched her major to math and left Carnegie Tech for Boston when she married Manuel Blum, who was then working at MIT and is now a professor of computer science at CMU.
		Blum's idea is to raise private and public funding for a center based at CMU where 50 scholars could work for two years on innovative technology projects that could possibly spin out as private commercial ventures.
	www.post-gazette.com /pg/05233/557060.stm (943 words)

	Up to the Challenge: Computer Scientists Crack a Set of AI-Based Codes
		CMU professor Manuel Blum's solution to the problem was Captchas, an acronym for Completely Automated Public Turing Test to Tell Computers and Humans Apart.
		Blum and his student Luis von Ahn posed a few sample Captchas as a challenge to the artificial intelligence community.
		Manuel Blum says that he is delighted that Gimpy was cracked, particularly since the researchers used a very general technique rather than a specialized program.
	www.siam.org /siamnews/11-02/gimpy.htm (1840 words)

	Blum to receive Turing Award
		Blum was honored "in recognition of his contributions to the foundation of computational complexity theory and its applications to cryptography and program checking," an ACM press release said.
		Blum is the University of California at Berkeley's Arthur J. Chick Professor in Electrical Engineering and Computing Sciences, a department in which he has served since 1968.
		Blum was born in Caracas, Venezuela, in 1938 and began his academic career at the Massachusetts Institute of Technology, where he received his B.S., M.S. and Ph.D. degrees.
	www.cra.org /CRN/html/9601/affiliate/none.4_1_m.shtml (238 words)

	Manuel Blum (Site not responding. Last check: 2007-09-06)
		Manuel Blum is a profound thinker, said ACM President...
		Blum was a retired partner with Fraoli, Blum and Yesselman which was responsible...
		Manuel Blum (26 de abril de 1938) es profesor de Ciencias de la Computación.
	enciclopedia.cc /Manuel_Blum (385 words)

	Blum Blum Shub - Encyclopedia, History, Geography and Biography (Site not responding. Last check: 2007-09-06)
		Blum Blum Shub - Encyclopedia, History, Geography and Biography
		GMPBBS (http://firefly.is-a-geek.org/gmpbbs/) - a GMP-based implementation of Blum Blum Shub.
		Blum Blum Shub, Security, References and External links.
	www.arikah.net /encyclopedia/Blum_Blum_Shub (349 words)

	11.08.95 - Gazette
		Manuel Blum, whose work on the limits of computers has had profound implications in areas such as computer security and problem-solving, has received the A.M. Turing Award.
		Blum, the Arthur J. Chick Professor in Electrical Engineering and Computing Sciences, has shown that secure business transactions, pseudo-random number generation and program checking are possible because all computational devices are limited by time or cost.
		Blum is the the third member of the faculty to receive the Turing Award in the past decade.
	www.berkeley.edu /news/berkeleyan/1995/1108/gazette.html (1188 words)

	Society for Neuroscience \| Archive
		Blum published more than 60 peer-reviewed papers and reviews, supervised five doctoral candidates and trained more than 12 post-doctoral fellows and visiting faculty members.
		The daughter of Lillian and Manuel Blum of Houston, Mariann Blum was born Jan. 19, 1955.
		Blum joined the faculty of Mount Sinai School of Medicine in New York in 1986 as an assistant professor in the Dr. Arthur M. Fishberg Research Center for Neurobiology.
	www.sfn.org /content/Membership1/MemberObituaries/ObituariesArchive/blum.html (454 words)

	Blum Blum Shub - Wikipedia, the free encyclopedia
		Blum Blum Shub (BBS) is a pseudorandom number generator proposed in 1986 by Lenore Blum, Manuel Blum and Michael Shub (Blum et al, 1986).
		GMPBBS - a GMP-based implementation of Blum Blum Shub.
		This page was last modified 03:34, 6 November 2005.
	en.wikipedia.org /wiki/Blum_Blum_Shub (331 words)

	DBLP: Manuel Blum (Site not responding. Last check: 2007-09-06)
		Manuel Blum, Alfredo De Santis, Silvio Micali, Giuseppe Persiano: Noninteractive Zero-Knowledge.
		Manuel Blum, Richard M. Karp, Oliver Vornberger, Christos H. Papadimitriou, Mihalis Yannakakis: The Complexity of Testing Whether a Graph is a Superconcentrator.
		Manuel Blum, Ashok K. Chandra, Mark N. Wegman: Equivalence of Free Boolean Graphs can be Decided Probabilistically in Polynomial Time.
	170.210.130.9 /root/public/SMOD9397/DBLP/db/indices/a-tree/b/Blum@Manuel.html (556 words)

	Computational Complexity: Understanding "Understanding"
		Blum made a strong point that his theory of consciousness is just being developed and emphasizing the word "towards" in the title.
		Blum modeled the goal as a difference between a pleasure and a pain function which looked to me like utility functions used by economists.
		Of Manuel's various accomplishments, what impresses me most is how successful a list of advisees he's had.
	weblog.fortnow.com /2005/06/understanding.html (1754 words)

	Robot solves Internet robot problem
		Manuel Blum was having trouble with his hand-held computer, so he turned to an Internet chat room for advice on how to recover a lost file.
		It's become a major problem on the Internet, as has the use of 'bots to register for e-mail addresses that are later used to send unwanted advertisements, or spam, to e-mail users.
		Blum's research team at Carnegie Mellon University has come up with a solution to the problem, one that the Web portal Yahoo implemented last month.
	www.postgazette.com /healthscience/20011021blumside1021p4.asp (519 words)

	National Academy of Sciences - Members (Site not responding. Last check: 2007-09-06)
		Blum is a computer and information scientist who has made seminal contributions to computational complexity theory and its applications to cryptography and program checking.
		He showed that secure business transactions and pseudo-random number generation are possible because of the finite resources of computational devices.
		Blum's theoretical breakthroughs have had many practical applications: as just one example, his "completely automated public Turing test" ensures that registrants to Web sites are humans and not robots.
	www4.nationalacademies.org /nas/naspub.nsf/(urllinks)/NAS-5HVGJ7?opendocument (261 words)

	Manuel The Manuel Barrueco Homepage. "a Major Artist With Remarkable Musicianship And A World Of Techniq (Site not responding. Last check: 2007-09-06)
		Manuel Puig nació en General Villegas, Provincia de Buenos Aires el 28 de diciembre de 1932 Es en esa ciudad donde Manuel Puig murió, el 22 de julio de 1990.
		Manuel Alvarez Bravo (Masters of Photography Series), Manuel Alvarez Bravo, A. Coleman "The photography of Manuel Alvarez Bravo is Mexican by cause, form, and content, anguish is omnipresent.
		Manuel recently was interviewed for the program "Colorado Matters" on Colorado Public Radio.
	www.99hosted.com /names19561.html (356 words)

	Blum
		In addition to these organisations, Blum is also a member of the American Mathematical Society, serving on its Council and she also as Vice President of the Society in 1990 - 1992.
		She represented the Society at the Pan African Congress of Mathematicians in Nairobi in the summer of 1991 and after this continued to work at building links between African and American mathematicians.
		Blum's important paper was Differentially closed fields: a model-theoretic tour which appeared in 1977 and, for the first time, made accessible some results she had found ten years earlier and included in her thesis.
	www.educ.fc.ul.pt /icm/icm2003/icm14/Blum.htm (1586 words)

	DB&LP: Manuel Blum (Site not responding. Last check: 2007-09-06)
		Lenore Blum, Manuel Blum: Toward a Mathematical Theory of Inductive Inference.
		Manuel Blum, William J. Sakoda: On the Capability of Finite Automata in 2 and 3 Dimensional Space.
		Manuel Blum, Dexter Kozen: On the Power of the Compass (or, Why Mazes Are Easier to Search than Graphs).
	smp2.cc.vt.edu /DB/db/indices/a-tree/b/Blum:Manuel.html (332 words)

	Is a BB&S System "Proven Secure"?
		Lenore Blum, Manuel Blum and Michael Shub (BB&S) are the authors of a famous mathematical article on the construction of an "unpredictable"
		Blum integers are the product of two distinct primes both congruent to 3 mod 4.
		Subject: Re: small subgroups in Blum Blum Shub Date: 21 Jun 2000 08:38:10 GMT From: pom@imsd.uni-mainz.de (Klaus Pommerening) Message-ID: <8iputi$o3o$3@bambi.zdv.Uni-Mainz.DE> References: <394ec029.4137859@news.io.com> Newsgroups: sci.crypt Lines: 36 In <394fa7b6.6164415@news.io.com> Terry Ritter wrote: > I do have a different model, but it is not a model of computation.
	www.ciphersbyritter.com /NEWS5/SUBGPBBS.HTM (18410 words)

	Computational Complexity: Favorite Theorems: Abstract Complexity
		Manuel Blum, A Machine-Independent Theory of the Complexity of Recursive Functions, JACM 1967.
		Though the axioms are very general, Blum shows their power with the speed-up theorem.
		Blum also showed there was a language that couldn't be sped up much and a computably-bounded relationship between any two abstract resource measures.
	weblog.fortnow.com /2005/08/favorite-theorems-abstract-complexity.html (442 words)

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