Julius Richard Büchi
Encyclopedia
Julius Richard Büchi was a Swiss logician and mathematician
.
He received his Dr. sc. nat. in 1950 at the ETH Zürich
under supervision of Paul Bernays
and Ferdinand Gonseth. Shortly afterwards he went to Purdue University
, Lafayette, Indiana
. He and his first student Lawrence Landweber
had a major influence on the development of theoretical computer science
.
Together with his friend Saunders Mac Lane
, a student of Paul Bernays
as well, Büchi published numerous celebrated works. He invented what is now known as the Büchi automaton
, a finite state automaton accepting certain collections of infinite words known as omega-regular languages. The "n squares' problem", known also as Büchi's problem
, is an open problem from number theory
, closely related to Hilbert's tenth problem
. One of his students was Lawrence Landweber
who received his doctorate at Purdue University in 1967.
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
.
He received his Dr. sc. nat. in 1950 at the ETH Zürich
ETH Zurich
The Swiss Federal Institute of Technology Zurich or ETH Zürich is an engineering, science, technology, mathematics and management university in the City of Zurich, Switzerland....
under supervision of Paul Bernays
Paul Bernays
Paul Isaac Bernays was a Swiss mathematician, who made significant contributions to mathematical logic, axiomatic set theory, and the philosophy of mathematics. He was an assistant to, and close collaborator of, David Hilbert.-Biography:Bernays spent his childhood in Berlin. Bernays attended the...
and Ferdinand Gonseth. Shortly afterwards he went to Purdue University
Purdue University
Purdue University, located in West Lafayette, Indiana, U.S., is the flagship university of the six-campus Purdue University system. Purdue was founded on May 6, 1869, as a land-grant university when the Indiana General Assembly, taking advantage of the Morrill Act, accepted a donation of land and...
, Lafayette, Indiana
Indiana
Indiana is a US state, admitted to the United States as the 19th on December 11, 1816. It is located in the Midwestern United States and Great Lakes Region. With 6,483,802 residents, the state is ranked 15th in population and 16th in population density. Indiana is ranked 38th in land area and is...
. He and his first student Lawrence Landweber
Lawrence Landweber
Lawrence H. Landweber is John P. Morgridge Professor Emeritus of Computer Science at the University of Wisconsin–Madison.He received his bachelor's degree in 1963 at Brooklyn College and his Ph.D. at Purdue University in 1967...
had a major influence on the development of theoretical computer science
Theoretical computer science
Theoretical computer science is a division or subset of general computer science and mathematics which focuses on more abstract or mathematical aspects of computing....
.
Together with his friend Saunders Mac Lane
Saunders Mac Lane
Saunders Mac Lane was an American mathematician who cofounded category theory with Samuel Eilenberg.-Career:...
, a student of Paul Bernays
Paul Bernays
Paul Isaac Bernays was a Swiss mathematician, who made significant contributions to mathematical logic, axiomatic set theory, and the philosophy of mathematics. He was an assistant to, and close collaborator of, David Hilbert.-Biography:Bernays spent his childhood in Berlin. Bernays attended the...
as well, Büchi published numerous celebrated works. He invented what is now known as the Büchi automaton
Büchi automaton
In computer science and automata theory, a Büchi automaton is a type of ω-automaton, which extends a finite automaton to infinite inputs. It accepts an infinite input sequence iff there exists a run of the automaton that visits one of the final states infinitely often. Büchi automata recognize the...
, a finite state automaton accepting certain collections of infinite words known as omega-regular languages. The "n squares' problem", known also as Büchi's problem
Büchi's Problem
Büchi's problem, also known as the n squares' problem, is an open problem from number theory named after the Swiss mathematician Julius Richard Büchi...
, is an open problem from number theory
Number theory
Number theory is a branch of pure mathematics devoted primarily to the study of the integers. Number theorists study prime numbers as well...
, closely related to Hilbert's tenth problem
Hilbert's tenth problem
Hilbert's tenth problem is the tenth on the list of Hilbert's problems of 1900. Its statement is as follows:Given a Diophantine equation with any number of unknown quantities and with rational integral numerical coefficients: To devise a process according to which it can be determined in a finite...
. One of his students was Lawrence Landweber
Lawrence Landweber
Lawrence H. Landweber is John P. Morgridge Professor Emeritus of Computer Science at the University of Wisconsin–Madison.He received his bachelor's degree in 1963 at Brooklyn College and his Ph.D. at Purdue University in 1967...
who received his doctorate at Purdue University in 1967.
Publications
- Finite Automata, Their Algebras and Grammars -- Towards a Theory of Formal Expressions. Published posthumously, Springer, New York 1989.
- Collected Papers of J. Richard Büchi. Edited by Saunders Mac Lane and Dirk Siefkes. Springer, New York 1990.