Upper and Lower Bounds on Continuous-Time Computation

  • Manuel Lameiras Campagnolo
  • Cristopher Moore
Part of the Discrete Mathematics and Theoretical Computer Science book series (DISCMATH)


We consider various extensions and modifications of Shannon’s General Purpose Analog Computer, which is a model of computation by differential equations in continuous time. We show that several classical computation classes have natural analog counterparts, including the primitive recursive functions, the elementary functions, the levels of the Grzegorczyk hierarchy, and the arithmetical and analytical hierarchies.


Elementary Function Turing Machine Recursive Function Algebraic Differential Equation Recursion Theory 
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Copyright information

© Springer-Verlag London 2001

Authors and Affiliations

  • Manuel Lameiras Campagnolo
    • 1
  • Cristopher Moore
    • 2
    • 3
    • 4
  1. 1.D.M./I.S.AUniversidade Técnica de UsboaTapada da Ajuda, LisboaPortugal
  2. 2.Computer Science DepartmentUniversity of New MexicoAlbuquerqueUSA
  3. 3.Physics and Astronomy DepartmentUniversity of New MexicoAlbuquerqueUSA
  4. 4.Santa Fe InstituteSanta FeUSA

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