Julius Richard Büchi (1924–1984) was a

Swiss Swiss most commonly refers to: * the adjectival form of Switzerland * Swiss people Swiss may also refer to: Places * Swiss, Missouri * Swiss, North Carolina * Swiss, West Virginia * Swiss, Wisconsin Other uses * Swiss Café, an old café located ...

logician 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, mathematical structure, structure, space, Mathematica ...

. He received his Dr. sc. nat. in 1950 at

ETH Zurich ETH Zurich (; ) is a public university in Zurich, Switzerland. Founded in 1854 with the stated mission to educate engineers and scientists, the university focuses primarily on science, technology, engineering, and mathematics. ETH Zurich ran ...

under the supervision of

Paul Bernays Paul Isaac Bernays ( ; ; 17 October 1888 – 18 September 1977) was a Swiss mathematician who made significant contributions to mathematical logic, axiomatic set theory, and the philosophy of mathematics. He was an assistant and close collaborator ...

and Ferdinand Gonseth. Shortly afterwards he went to

Purdue University Purdue University is a Public university#United States, public Land-grant university, land-grant research university in West Lafayette, Indiana, United States, and the flagship campus of the Purdue University system. The university was founded ...

in Lafayette,

Indiana Indiana ( ) is a U.S. state, state in the Midwestern United States, Midwestern region of the United States. It borders Lake Michigan to the northwest, Michigan to the north and northeast, Ohio to the east, the Ohio River and Kentucky to the s ...

. He and his first student Lawrence Landweber had a major influence on the development of

theoretical computer science Theoretical computer science is a subfield of computer science and mathematics that focuses on the Abstraction, abstract and mathematical foundations of computation. It is difficult to circumscribe the theoretical areas precisely. The Associati ...

. Together with his friend

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

, a student of

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 mach ...

, 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 languages. The "''n'' squares' problem", known also as

Büchi's problem In number theory, Büchi's problem, also known as the ''n'' squares' problem, is an open problem named after the Swiss mathematician Julius Richard Büchi. It asks whether there is a positive integer ''M'' such that every sequence of ''M'' or mo ...

, is an open problem from

number theory Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. Number theorists study prime numbers as well as the properties of mathematical objects constructed from integers (for example ...

, closely related to Hilbert's tenth problem.

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