John Myhill

Born

(1923-08-11)11 August 1923

Birmingham, United Kingdom

Died

15 February 1987(1987-02-15) (aged 63)

Nationality

British

Fields

Mathematics

Alma mater

Harvard University

Thesis

A Semantically Complete Foundation for Logic and Mathematics (1949)

Doctoral advisor

Willard Van Orman Quine

Lynn Harold Loomis

Doctoral students

Erik Ellentuck

Andre Scedrov

Spouse

Akiko Kino (died 1983)

Children

John (born 1957), Robert (born 1960), Phoebe (born 1963), Nova (born 1970)[1]

John R. Myhill, Sr. (11 August 1923 – 15 February 1987[2]) was a British mathematician.

Contents

1 Education

2 Research results

3 See also

4 References

Education[edit]

Myhill received his Ph.D. from Harvard University under Willard Van Orman Quine in 1949.[3] He was professor at SUNY Buffalo from 1966 until his death in 1987. He also taught at several other universities.

His son, also called John Myhill, is a professor of linguistics in the English department of the University of Haifa in Israel.

Research results[edit]

In the theory of formal languages, the Myhill–Nerode theorem, proven by Myhill with Anil Nerode, characterizes the regular languages as the languages that have only finitely many inequivalent prefixes.

In computability theory, the Rice–Myhill–Shapiro theorem, more commonly known as Rice’s theorem, states that, for any nontrivial property P of partial functions, it is undecidable to determine whether a given Turing machine computes a function with property P. The Myhill isomorphism theorem is a computability-theoretic analogue of the Cantor–Bernstein–Schroeder theorem that characterizes the recursive isomorphisms of pairs of sets.

In the theory of cellular automata, Myhill is known for proving (along with E. F. Moore) the Garden of Eden theorem, stating that a cellular automaton has a configuration with no predecessor if and only if it has two different asymptotic configurations which evolve to the same configuration. He is also known for posing the firing squad synchronization problem of designing an automaton that, starting from a single non-quiescent cell, evolves to a configuration in which all cells reach the same non-quiescent state at the same time; this problem was again solved by Moore.

In constructive set theory, Myhill is known for proposing an axiom system that avoids the axiom of choice and the law of the excluded middle, known as Intuitionistic Zermelo–Fraenkel. He also developed a constructive set t

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