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The complexity of analog computation

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  • Vergis, Anastasios
  • Steiglitz, Kenneth
  • Dickinson, Bradley

Abstract

We ask if analog computers can solve NP-complete problems efficiently. Regarding this as unlikely, we formulate a strong version of Church's Thesis: that any analog computer can be simulated efficiently (in polynomial time) by a digital computer. From this assumption and the assumption that P ≠ NP we can draw conclusions about the operation of physical devices used for computation.

Suggested Citation

  • Vergis, Anastasios & Steiglitz, Kenneth & Dickinson, Bradley, 1986. "The complexity of analog computation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 28(2), pages 91-113.
    • Handle: RePEc:eee:matcom:v:28:y:1986:i:2:p:91-113
    DOI: 10.1016/0378-4754(86)90105-9
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    References listed on IDEAS

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    1. William Miehle, 1958. "Link-Length Minimization in Networks," Operations Research, INFORMS, vol. 6(2), pages 232-243, April.
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    Cited by:

    1. Manuel Campagnolo & Cristopher Moore, 2000. "Upper and Lower Bounds on Continuous-Time Computation," Working Papers 00-06-030, Santa Fe Institute.
    2. Manuel Lameiras Campagnolo & Cristopher Moore & José Félix Costa, 1999. "Iteration, Inequalities, and Differentiability in Analog Computers," Working Papers 99-07-043, Santa Fe Institute.

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