Julius Richard Büchi (1924–1984) was a Swiss

logician Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from premises ...

and

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

. He received his Dr. sc. nat. in 1950 at ETH Zurich under the supervision of Paul Bernays and

Ferdinand Gonseth Ferdinand Gonseth (1890–1975) was a Swiss mathematician and philosopher. He was born on 22 September 1890 at Sonvilier, the son of Ferdinand Gonseth, a clockmaker, and his wife Marie Bourquin. He studied at La Chaux-de-Fonds, and read physics a ...

. Shortly afterwards he went to

Purdue University Purdue University is a public land-grant research university in West Lafayette, Indiana, and the flagship campus of the Purdue University system. The university was founded in 1869 after Lafayette businessman John Purdue donated land and mone ...

Lafayette Lafayette or La Fayette may refer to: People * Lafayette (name), a list of people with the surname Lafayette or La Fayette or the given name Lafayette * House of La Fayette, a French noble family ** Gilbert du Motier, Marquis de Lafayette (1757� ...

Indiana Indiana () is a U.S. state in the Midwestern United States. It is the 38th-largest by area and the 17th-most populous of the 50 States. Its capital and largest city is Indianapolis. Indiana was admitted to the United States as the 19th s ...

. He and his first student

Lawrence Landweber Lawrence Hugh 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. His doct ...

had a major influence on the development of

theoretical computer science computer science (TCS) is a subset of general computer science and mathematics that focuses on mathematical aspects of computer science such as the theory of computation, lambda calculus, and type theory. It is difficult to circumscribe the ...

. Together with his friend

Saunders Mac Lane Saunders Mac Lane (4 August 1909 – 14 April 2005) was an American mathematician who co-founded category theory with Samuel Eilenberg. Early life and education Mac Lane was born in Norwich, Connecticut, near where his family lived in Taftville ...

, a student of Paul Bernays as well, Büchi published numerous celebrated works. He invented what is now known as the

Büchi automaton In computer science and automata theory, a deterministic Büchi automaton is a theoretical machine which either accepts or rejects infinite inputs. Such a machine has a set of states and a transition function, which determines which state the machi ...

, a

finite-state machine A finite-state machine (FSM) or finite-state automaton (FSA, plural: ''automata''), finite automaton, or simply a state machine, is a mathematical model of computation. It is an abstract machine that can be in exactly one of a finite number o ...

accepting certain sets of infinite sequences of characters known as

omega-regular language The ω-regular languages are a class of ω-languages that generalize the definition of regular languages to infinite words. Formal definition An ω-language ''L'' is ω-regular if it has the form * ''A''ω where ''A'' is a regular language n ...

s. The "''n'' squares' problem", known also as Büchi's problem, is an open problem from

number theory Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and integer-valued functions. German mathematician Carl Friedrich Gauss (1777–1855) said, "Mat ...

, closely related to

Hilbert's tenth problem Hilbert's tenth problem is the tenth on the list of mathematical problems that the German mathematician David Hilbert posed in 1900. It is the challenge to provide a general algorithm which, for any given Diophantine equation (a polynomial equa ...

Selected publications

*''Finite Automata, Their Algebras and Grammars – Towards a Theory of Formal Expressions''. Published posthumously, Springer, New York 1989. *''Collected Works of J. Richard Büchi''. Edited by Saunders Mac Lane and Dirk Siefkes. Springer, New York 1990.

External links

* 1924 births 1984 deaths 20th-century Swiss mathematicians Purdue University alumni Swiss expatriates in the United States {{mathematician-stub