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". April 26 is the 116th day of the year in the Gregorian Calendar (117th in leap years). ... 1938 (MCMXXXVIII) was a common year starting on Saturday (link will take you to calendar). ... City motto: Ave María Santísima, sin pecado concebida, en el primer instante de su ser natural. ... Computer science (informally: CS or compsci) is, in its most general sense, the study of computation and information processing, both in hardware and in software. ... The A.M. Turing Award is given annually by the Association for Computing Machinery to a person selected for contributions of a technical nature made to the computing community. ... In computer science, computational complexity theory is the branch of the theory of computation that studies the resources required during computation to solve a given problem. ... Cryptography has had a long and colourful history. ...

Biography

Blum attended MIT, where he received his bachelor's degree and his master's degree in EECS in 1959 and 1961 respectively, and his Ph.D. in Mathematics in 1964 under professor Marvin Minsky. The Massachusetts Institute of Technology, or MIT, is a research and educational institution located in the city of Cambridge, Massachusetts, USA. MIT is a world leader in science and technology, as well as in many other fields, including management, economics, linguistics, political science, and philosophy. ... A bachelors degree is usually an undergraduate academic degree awarded for a course or major that generally lasts three or four years. ... A masters degree is an academic degree usually awarded for completion of a postgraduate or graduate course of one to three years in duration. ... 1959 (MCMLIX) was a common year starting on Thursday of the Gregorian calendar. ... 1961 (MCMLXI) was a common year starting on Sunday (link will take you to calendar). ... Doctor of Philosophy, or Ph. ... Wikibooks Wikiversity has more about this subject: School of Mathematics Wikiquote has a collection of quotations related to: Mathematics Look up Mathematics in Wiktionary, the free dictionary Wikimedia Commons has media related to: Mathematics Inter. ... For the Nintendo 64 emulator, see 1964 (Emulator). ... Marvin Minsky Marvin Lee Minsky (born August 9, 1927), sometimes affectionately known as Old Man Minsky, is an American scientist in the field of artificial intelligence (AI), co-founder of MITs AI laboratory, and author of several texts on AI and philosophy. ...

He worked as a professor of computer science at the University of California, Berkeley until 2000. University of California, Berkeley The University of California, Berkeley (also known as Cal, UCB, UC Berkeley, The University of California, California, or simply Berkeley) is a public coeducational university situated east of the San Francisco Bay in Berkeley, California, overlooking the Golden Gate. ... This article is about the year 2000. ...

He is currently the Bruce Nelson Professor of Computer Science at Carnegie Mellon University, where his wife, Lenore Blum, and son, Avrim Blum, are also professors of Computer Science. Carnegie Mellon University Carnegie Mellon University is a private research university located in Pittsburgh, Pennsylvania. ... Lenore Blum received her Ph. ...

Work

In the 60s he developed an axiomatic complexity theory which was independent of concrete machine models. The theory is based on Gödel numberings and the Blum axioms. Even though the theory is not based on any machine model it yields concrete results like the compression theorem, the gap theorem, the honesty theorem and the celebrated Blum speedup theorem. In formal number theory a Gödel numbering is a function which assigns to each symbol and formula of some formal language a unique natural number called a Gödel number (GN). ... In computational complexity theory the Blum axioms or Blum complexity axioms are axioms which specify desirable properties of complexity measures on the set of computable functions. ... In computational complexity theory the compression theorem is an important theorem about the complexity of computable functions. ... In computational complexity theory the Gap theorem is an important theorem about the complexity of computable functions. ... In computational complexity theory Blums speedup theorem, first stated by Manuel Blum in 1967, is an important theorem about the complexity of computable functions. ...

Some of his work includes the Blum Blum Shub pseudorandom number generator, the Blum-Goldwasser cryptosystem, and more recently CAPTCHAs. Blum Blum Shub (BBS) is a pseudorandom number generator proposed in 1986 by Lenore Blum, Manuel Blum and Michael Shub (Blum et al, 1986). ... The Blum-Goldwasser (BG) cryptosystem is an asymmetric key encryption algorithm proposed by Manuel Blum and Shafi Goldwasser in 1984. ... A captcha (an acronym for completely automated public Turing test to tell computers and humans apart) is a type of challenge-response test used in computing to determine whether or not the user is human. ...

See also

• Blum complexity axioms
• Blum's speedup theorem
• Blum Blum Shub
• Blum-Goldwasser cryptosystem

In computational complexity theory the Blum axioms or Blum complexity axioms are axioms which specify desirable properties of complexity measures on the set of computable functions. ... In computational complexity theory Blums speedup theorem, first stated by Manuel Blum in 1967, is an important theorem about the complexity of computable functions. ... Blum Blum Shub (BBS) is a pseudorandom number generator proposed in 1986 by Lenore Blum, Manuel Blum and Michael Shub (Blum et al, 1986). ... The Blum-Goldwasser (BG) cryptosystem is an asymmetric key encryption algorithm proposed by Manuel Blum and Shafi Goldwasser in 1984. ...

External links

Blum's home pages:

• Carnegie Mellon page
• Berkeley page (outdated)