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The Work of Anil Nerode: A Retrospective

  • J. B. Remmel
  • J. N. Crossley
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Part of the Progress in Computer Science and Applied Logic book series (PCS, volume 12)

Abstract

Anil Nerode’s work divides into a number of periods though, inevitably, there are overlaps and cross-currents. In this survey we indicate what we consider the highlights so far in mathematics and computer science. (We have not included his work in environmental science policy for the United States Environmental Protection Agency, except insofar as it is listed in the bibliography at the end (Loehr, Goldstein, Nerode & Risser [1992]).) We distinguish six periods or areas: 1. His thesis and early work in automata theory and recursion theory, 2. Isols, 3. Undecidability, 4. Recursive algebra, 5. Polynomial-time structures and 6. Computer science. From the authors’ personal experience, we know that much of Nerode’s effort has gone into developing foundations for various subjects. This, of course, means that a lot of his work has involved not only proving theorems but searching for the appropriate basic definitions which allow an area to be developed. Even though our space is limited, we hope to give some sense of this foundational work in this survey. Finally we should note that Nerode has made contributions to logic in general by his influence on other researchers in the field. This not only includes the 34 Ph.D. students that he has supervised to date, but also many researchers in logic who have benefited from his suggestions for areas of research to pursue, or approaches to a problem, as well as his enthusiastic encouragement of their efforts.

Keywords

Boolean Algebra Logic Programming Default Logic Recursive Tree Deterministic Finite Automaton 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Thesis

  1. Nerode, A. [1956], Composita, Equations, and Recursive Definitions. Ph.D. Thesis, University of Chicago.Google Scholar

Books Written

  1. Crossley, J.N. and A. Nerode [1974], Combinatorial Functors. Ergebnisse der Math. und ihrer Grenzgebiete, 81, Springer-Verlag, New York-Heidelberg.zbMATHGoogle Scholar
  2. Nerode, A. and R. Shore [1993], Logic and Applications. Springer-Verlag.Google Scholar
  3. Nerode, A. and G. Odifreddi. Lambda Calculi and Constructive Logics. MSI Technical Report’ 90-55. To be published by MIT press in 1994.Google Scholar

Books Edited

  1. Nerode, A. and R. Shore (eds.) [1985], Recursion Theory. Proc. Symp. in Pure Mathematics, 42, American Math. Soc., Providence, RI.zbMATHGoogle Scholar
  2. Nerode, A., A. Marek and V.S. Subrahmanian (eds.) [1991], Logic Programming and Non-Motononic Reasoning. MIT Press, Cambridge, MA.Google Scholar
  3. Nerode, A. (ed.) [1992], Myhill Memorial Volume. Annals of Pure & Appl. Logic, 56.Google Scholar
  4. Taitslin, M. and A. Nerode (eds.) [1992], Logical Foundations of Computer Science: Proceedings of a Symposium in Tver, Russia. Lecture Notes in Computer Science, Springer-Verlag, Berlin.Google Scholar
  5. Pereira, L. and A. Nerode [eds.] [1993], Logic Programming and Nonmonotonic Reasoning. Proc. 2nd International Workshop, MIT Press.Google Scholar
  6. Ershov, Y.L., S.S. Goncharov, A. Nerode and J.B. Remmel (eds.) [in preparation], Recursive Mathematics.Google Scholar

Papers

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  29. Jutro, P., P. Lavori, A. Nerode and S. Sievers [1982], Risk Assessment for Toxic Substances: Exploratory Data Analysis for Cadmium. Environmental Professional, 4, 351–364.Google Scholar
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  52. Nerode, A. and J.B. Remmel [1990c], Complexity-Theoretic Algebra: Bases of Vector Spaces. In: Feasible Mathematics, S. Buss & P. Scott (eds.), Springer.Google Scholar
  53. Marek, W., A. Nerode and J.B. Remmel [1991], A Context for Belief Revision: Normal Logic Programs. MSI Tech. Report 91-63, appears in vl. 991, Workshop on Defeasible Reasoning, of the North-American Logic Programming Association, November 1991.Google Scholar
  54. Nerode, A. [1991], Some Lectures on modal logic. In: Logic, Algebra, and Computation, F.L. Brauer (ed.), Springer-Verlag, 281–334.Google Scholar
  55. Nerode, A. and J.B. Remmel [1991], A model for hybrid systems. Notes of a Hybrid Systems Workshop, MSI, Cornell University, Ithaca, NY.Google Scholar
  56. Nerode, A., A. Yakhnis and V. Yakhnis [1991], Concurrent Programs as Strategies in games. In: Logic from Computer Science (Y. Moschovakis ed.), MSRI Series, Springer-Verlag.Google Scholar
  57. Bell, C., A. Nerode, R.T. Ng and V.S. Subrahmanian [1992], Implementing Deductive Databases by Linear Programming. MSI Technical Report, Cornell University. Submitted to ACM Transactions on Database Systems.Google Scholar
  58. Kohn, W. and A. Nerode [1992], An Autonomous Control Theory: An Overview. 7992 IEEE Symposium on Computer Aided Control System Design (March 17-19, 1992, Napa Valley, CA), 204–210, from IEEE Services Center, 445 Hoes Lane, Piscataway, NJ 08854.Google Scholar
  59. Loehr, R.C., B.D. Goldstein, A. Nerode and P.G. Risser [1992], Safeguarding the Future: Credible Science, Credible Decisions. Report of the Expert Panel on the Role of Science at EPA, United States Environmental Protection Agency 600/9-91/050, 52 pp.Google Scholar
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  63. Nerode, A., R. Emery and V.S. Subrahmanian [1992], Computing circumscriptive databases, part II: optimization, implementation, and experimentation. MSI Technical Report.Google Scholar
  64. Nerode, A. and Xiaolin Ge [1992], Turing located sets. MSI Technical Report.Google Scholar
  65. Nerode, A. and Xiaolin Ge [1992], Constructive extreme points for Krein-Milman Theorem. MSI Technical Report.Google Scholar
  66. Nerode, A. and J. Guckenheimer [1992], Simulation for hybrid systems and nonlinear control. CDC92.Google Scholar
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  68. Nerode, A., J. Lu, J.B. Remmel and V.S. Subrahmanian [1992], Hybrid knowledge bases. MSI Technical Report.Google Scholar
  69. Nerode, A., R.T. Ng and V.S. Subrahmanian [1992], Computing Circumscriptive Databases, Part I: Theory and Algorithms. MSI Tech. Report 92-2, Cornell University, 40 pp. To appear in Information and Computation.Google Scholar
  70. Nerode, A. and A. Yakhnis [1992], Modelling hybrid systems as games. CDC92.Google Scholar
  71. W. Kohn and A. Nerode [this volume], Multiple Agent Autonomous Hybrid Control Systems.Google Scholar
  72. Marek, W., A. Nerode and J.B. Remmel [1993a], Forward chaining normal nonmonotonic rule systems: a context for belief revision. To appear in Annals of Pure & Appl. Logic.Google Scholar
  73. Marek, W., A. Nerode and J.B. Remmel [1993b], Computing jumps with an FC-normal nonmonotonic rule system. In preparation.Google Scholar
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  76. Nerode, A., J.B. Remmel and A. Yakhnis [1993], Hybrid systems and continuous sensing games. To appear in Proc. 8th IEEE Internat. Symposium on Intelligence Control, Chicago, Ill., 1993.Google Scholar
  77. Nerode, A., J.B. Remmel and A. Yakhnis [1993], Playing games on graphs: extracting concurrent and hybrid control programs. In preparation.Google Scholar
  78. Nerode, A., A. Yakhnis and V. Yakhnis [this volume], Distributed Concurrent Programs as Strategies in Games.Google Scholar
  79. Kagan, V., A. Nerode and V.S. Subrahmanian [to appear], Computing definite logic programs by partial instantiation [to appear]. In: Tver 92 Volume. Annals of Pure & Appl. Logic.Google Scholar
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Copyright information

© Springer Science+Business Media New York 1993

Authors and Affiliations

  • J. B. Remmel
    • 1
  • J. N. Crossley
    • 2
  1. 1.Department of MathematicsUniversity of California at San DiegoLa JollaUSA
  2. 2.Department of Mathematics and Department of Computer ScienceMonash UniversityClaytonAustralia

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