NDLI: Genericity, Randomness, and Polynomial-Time Approximations

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Wang, Yongge
Copyright Year	1998
Abstract	Polynomial-time safe and unsafe approximations for intractable sets were introduced by Meyer and Paterson [Technical Report TM-126, Laboratory for Computer Science, MIT, Cambridge, MA, 1979] and Yesha [SIAM J. Comput., 12 (1983), pp. 411--425], respectively. The question of which sets have optimal safe and unsafe approximations has been investigated extensively. Duris and Rolim [Lecture Notes in Comput. Sci. 841, Springer-Verlag, Berlin, New York, 1994, pp. 38--51] and Ambos-Spies [Proc. 22nd ICALP, Springer-Verlag, Berlin, New York, 1995, pp. 384--392] showed that the existence of optimal polynomial-time approximations for the safe and unsafe cases is independent. Using the law of the iterated logarithm for p-random sequences (which has been recently proven in [Proc. 11th Conf. Computational Complexity, IEEE Computer Society Press, Piscataway, NJ, 1996, pp. 180--189]), we extend this observation by showing that both the class of polynomial-time $\Delta$-levelable sets and the class of sets which have optimal polynomial-time unsafe approximations have p-measure 0. Hence typical sets in E (in the sense of p-measure) do not have optimal polynomial-time unsafe approximations. We will also establish the relationship between resource bounded genericity concepts and the polynomial-time safe and unsafe approximation concepts.
Starting Page	394
Ending Page	408
Page Count	15
File Format	PDF
ISSN	00975397
DOI	10.1137/S009753979630235X
e-ISSN	10957111
Journal	SIAM Journal on Computing (SMJCAT)
Issue Number	2
Volume Number	28
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2006-07-28
Access Restriction	Subscribed
Subject Keyword	Models of computation resource bounded genericity resource bounded randomness approximation Analysis of algorithms and problem complexity Complexity of computation computational complexity Algorithmic information theory
Content Type	Text
Resource Type	Article
Subject	Mathematics Computer Science

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