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Genericity and Randomness over Feasible Probability Measures

In: Advances in Algorithms, Languages, and Complexity

Author

Listed:
  • Amy K. Lorentz

    (Hewlett-Packard Company, Color LaserJet and Consumables Division)

  • Jack H. Lutz

    (Iowa State University, Department of Computer Science)

Abstract

This paper investigates the notion of resource-bounded genericity developed by Ambos-Spies, Fleischhack, and Huwig. Ambos-Spies, Neis, and Terwijn have recently shown that every language that is t(n)-random over the uniform probability measure is t(n)-generic. It is shown here that, in fact, every language that is t(n)-random over any strongly positive, t(n)-computable probability measure is t(n)-generic. Roughly speaking, this implies that, when genericity is used to prove a resource-bounded measure result, the result is not specific to the underlying probability measure.

Suggested Citation

  • Amy K. Lorentz & Jack H. Lutz, 1997. "Genericity and Randomness over Feasible Probability Measures," Springer Books, in: Ding-Zhu Du & Ker-I Ko (ed.), Advances in Algorithms, Languages, and Complexity, pages 171-187, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4613-3394-4_8
    DOI: 10.1007/978-1-4613-3394-4_8
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