# Anil Nerode

**Anil Nerode** (born 1932) is an American mathematician. He received his undergraduate education and a Ph.D. in mathematics from the University of Chicago, the latter under the directions of Saunders Mac Lane. 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 in many-sorted free algebras and its relation to equational definitions of the partial recursive functions.[1]

While in graduate school, beginning in 1954, he worked at Prof. 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 Summer 1957 Institute in Logic. In 1958 to 1959 he went to the Institute for Advanced Study in Princeton, New Jersey, where he worked with Kurt Gödel.

Nerode is Goldwin Smith Professor of Mathematics at Cornell University. His interests are in mathematical logic, the theory of automata, computability and complexity theory, the calculus of variations, and distributed systems. With John Myhill, Nerode proved the Myhill–Nerode theorem specifying necessary and sufficient conditions for a formal language to be regular.[2]

Nerode is an Editorial Board member of the journals *Annals of Mathematics and Artificial Intelligence*,[3] *Mathematical and Computer Modelling*,[4] *Documenta Mathematica*[5] and others.

In 2012 he became a fellow of the American Mathematical Society.[6]

## Notes

- For a description of Nerode's mathematical work until 1992, see "The Work of Anil Nerode: A Retrospective" co-authored by Nerode's former student J. B. Remmel and J.N. Crossley, which appears in the 1992 Festschrift volume "Logical Methods: in honor of Anil Nerode's Sixtieth Birthday" (J. N. Crossley, Jeffrey B. Remmel, Richard A. Shore, and Moss E. Sweedler, eds., Birkhäuser, 1993, ISBN 0-8176-3690-0).
- Martin Davis, Elaine J. Weyuker,
*Computability, Complexity, and Languages: Fundamentals of Theoretical Computer Science.*Elsevier, 1994, ISBN 978-0-12-206382-4; Ch. 7. Myhill-Nerode theorem. - Editorial Board,
*Annals of Mathematics and Artificial Intelligence*, Springer-Verlag. Accessed January 21, 2010 - Editorial Board,
*Mathematical and Computer Modelling*, Elsevier. Accessed January 21, 2010. - Editorial Board Archived 2013-01-21 at the Wayback Machine,
*Documenta Mathematica*, University of Illinois. Accessed January 21, 2010 - List of Fellows of the American Mathematical Society, retrieved 2013-02-24.

## References

- John E. Hopcroft and Jeffrey D. Ullman,
*Introduction to Automata Theory, Languages, and Computation*, Addison-Wesley Publishing, Reading Massachusetts, 1979. ISBN 0-201-02988-X.*(See chapter 3 for Myhill-Nerode theorem)* - Anil Nerode at the Mathematics Genealogy Project