Anil Nerode
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Anil Nerode (born 1932) is an American
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 ...
, known for his work in
mathematical logic Mathematical logic is the study of Logic#Formal logic, formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory (also known as computability theory). Research in mathematical logic com ...
and for his many-decades tenure as a professor at
Cornell University Cornell University is a Private university, private Ivy League research university based in Ithaca, New York, United States. The university was co-founded by American philanthropist Ezra Cornell and historian and educator Andrew Dickson W ...
. He received his undergraduate education and a Ph.D. in mathematics from the
University of Chicago The University of Chicago (UChicago, Chicago, or UChi) is a Private university, private research university in Chicago, Illinois, United States. Its main campus is in the Hyde Park, Chicago, Hyde Park neighborhood on Chicago's South Side, Chic ...
, the latter under the directions of
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 ...
. He enrolled in the Hutchins College at the University of Chicago in 1947 at the age of 15, and received his Ph.D. in 1956. His Ph.D. thesis was on an algebraic abstract formulation of
substitution Substitution may refer to: Arts and media *Substitution (poetry), a variation in poetic scansion * Substitution (theatre), an acting methodology Music *Chord substitution, swapping one chord for a related one within a chord progression *Tritone ...
in many-sorted
free algebra In mathematics, especially in the area of abstract algebra known as ring theory, a free algebra is the noncommutative analogue of a polynomial ring since its elements may be described as "polynomials" with non-commuting variables. Likewise, the ...
s and its relation to equational definitions of the
partial recursive function In mathematical logic and computer science, a general recursive function, partial recursive function, or μ-recursive function is a partial function from natural numbers to natural numbers that is "computable" in an intuitive sense – as well as i ...
s. While in graduate school, beginning in 1954, he worked at Professor Walter Bartky's Institute for Air Weapons Research, which did classified work for the US Air Force. He continued to work there following the completion of his Ph.D., from 1956 to 1957. In the summer of 1957 he attended the Cornell
NSF NSF may stand for: Political organizations *National Socialist Front, a Swedish National Socialist party *NS-Frauenschaft, the women's wing of the former German Nazi party * National Students Federation, a leftist Pakistani students' political g ...
Summer 1957 Institute in Logic. In 1958 to 1959 he went to the
Institute for Advanced Study The Institute for Advanced Study (IAS) is an independent center for theoretical research and intellectual inquiry located in Princeton, New Jersey. It has served as the academic home of internationally preeminent scholars, including Albert Ein ...
in Princeton, New Jersey, where he worked with
Kurt Gödel Kurt Friedrich Gödel ( ; ; April 28, 1906 – January 14, 1978) was a logician, mathematician, and philosopher. Considered along with Aristotle and Gottlob Frege to be one of the most significant logicians in history, Gödel profoundly ...
. He also did post-graduate work at
University of California, Berkeley The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California), is a Public university, public Land-grant university, land-grant research university in Berkeley, California, United States. Founded in 1868 and named after t ...
. When in 1959 he got an unsolicited offer of a faculty position at
Cornell University Cornell University is a Private university, private Ivy League research university based in Ithaca, New York, United States. The university was co-founded by American philanthropist Ezra Cornell and historian and educator Andrew Dickson W ...
, he accepted, in part because on his previous visit to the campus he had thought "it was the prettiest place I'd ever seen". Nerode is a distinguished professor of arts and sciences in mathematics at Cornell. He was formerly Goldwin Smith Professor of Mathematics at Cornell, having been named to that chair in 1991. His interests are in
mathematical logic Mathematical logic is the study of Logic#Formal logic, formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory (also known as computability theory). Research in mathematical logic com ...
, the
theory of automata Automata theory is the study of abstract machines and automaton, automata, as well as the computational problems that can be solved using them. It is a theory in theoretical computer science with close connections to cognitive science and math ...
,
computability Computability is the ability to solve a problem by an effective procedure. It is a key topic of the field of computability theory within mathematical logic and the theory of computation within computer science. The computability of a problem is c ...
and complexity theory, the
calculus of variations The calculus of variations (or variational calculus) is a field of mathematical analysis that uses variations, which are small changes in Function (mathematics), functions and functional (mathematics), functionals, to find maxima and minima of f ...
, and
distributed system Distributed computing is a field of computer science that studies distributed systems, defined as computer systems whose inter-communicating components are located on different networked computers. The components of a distributed system commun ...
s. With
John Myhill John R. Myhill Sr. (11 August 1923 – 15 February 1987) was a British mathematician. Education Myhill received his Ph.D. from Harvard University under the supervision of Willard Van Orman Quine in 1949. He was a professor at SUNY Buffalo fro ...
, Nerode proved the
Myhill–Nerode theorem In the theory of formal languages, the Myhill–Nerode theorem provides a necessary and sufficient condition for a language to be regular. The theorem is named for John Myhill and Anil Nerode, who proved it at the University of Chicago in 1957 . ...
specifying necessary and sufficient conditions for a
formal language In logic, mathematics, computer science, and linguistics, a formal language is a set of strings whose symbols are taken from a set called "alphabet". The alphabet of a formal language consists of symbols that concatenate into strings (also c ...
to be
regular Regular may refer to: Arts, entertainment, and media Music * "Regular" (Badfinger song) * Regular tunings of stringed instruments, tunings with equal intervals between the paired notes of successive open strings Other uses * Regular character, ...
. With
Bakhadyr Khoussainov Bakhadyr M. Khoussainov () is a computer scientist and mathematician, who was born and educated in the Soviet Union, works in the fields of mathematical logic, computability theory, computable model theory and theoretical computer science. With Anil ...
, Nerode founded the theory of automatic structures, an extension of the theory of
automatic group In mathematics, an automatic group is a finitely generated group equipped with several finite-state automata. These automata represent the Cayley graph of the group. That is, they can tell whether a given word representation of a group element is ...
s. The academic year 2019–20 saw Nerode's 60th year as an active faculty member at Cornell, which the university said was its longest such tenure ever. Also published in ''Math Matters'' newsletter, Cornell University Department of Mathematics, January 2020, p. 2. In 2022, the Nerode-90 conference was held online to celebrate his contributions to the field.''Math Matters'' newsletter, Cornell University Department of Mathematics, Winter 2022–2023, p. 10. Nerode is an Editorial Board member of the journals ''Annals of Mathematics and Artificial Intelligence'', ''Mathematical and Computer Modelling'', ''Documenta Mathematica'' and others. In 2012 he became a fellow of the
American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...
.List of Fellows of the American Mathematical Society
retrieved 2013-02-24.


Notes


References

* John E. Hopcroft and Jeffrey D. Ullman, ''
Introduction to Automata Theory, Languages, and Computation #REDIRECT Introduction to Automata Theory, Languages, and Computation {{R from other capitalisation ...
'', Addison-Wesley Publishing, Reading Massachusetts, 1979. . ''(See chapter 3 for Myhill-Nerode theorem)''


External links


Anil Nerode's homepage
{{DEFAULTSORT:Nerode, Anil 1932 births University of Chicago alumni 20th-century American mathematicians 21st-century American mathematicians American computer scientists Cornell University faculty Living people Fellows of the American Mathematical Society American academics of Indian descent