NDLI: Self-P-Printability and Polynomial Time Turing Equivalence to a Tally Set

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Self-P-Printability and Polynomial Time Turing Equivalence to a Tally Set

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Subinstein, Roy S.
Copyright Year	1991
Abstract	The class of self-P-printable sets, those sets that are enumerable in polynomial time relative to themselves, has been shown to be the same as the class of sets that have small generalized Kolmogorov complexity relative to themselves [J. Hartmanis and L. Hemachandra, Proc. 3rd Annual Symposium on Theoretical Aspects of Computer Science, Springer-Verlag, Berlin, New York, 1986, pp. 321333] and [J. Balczar and R. Book, Acta Informatics, 23 (1986), pp. 679688]. This class properly includes the sets of small generalized Kolmogorov complexity, including the tally sets. The class of sets polynomial time Turing equivalent to a tally set includes the class of self-P-printable sets [J. Balczar and R. Book, op. cit.], and the inclusion is clearly proper because every self-P-printable set must be sparse while there are many nonsparse sets (such as all nonsparse sets in P) that are polynomial time Turing equivalent to a tally set.The question of whether or not the class of self-P-printable sets is the same as the class of sparse sets that are polynomial time Turing equivalent to a tally set is addressed here. Necessary and sufficient conditions for the equivalence of these two classes are presented. Also presented are relativizations for all possible combinations of these necessary and sufficient conditions, suggesting that the nonrelativized solution to the question of this equivalence will be difficult to determine.
Starting Page	1021
Ending Page	1033
Page Count	13
File Format	PDF
ISSN	00975397
DOI	10.1137/0220064
e-ISSN	10957111
Journal	SIAM Journal on Computing (SMJCAT)
Issue Number	6
Volume Number	20
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2006-07-13
Access Restriction	Subscribed
Subject Keyword	Models of computation sparse sets P-printable sets relativization Kolmogorov complexity Complexity of computation tally sets computational complexity Complexity classes Algorithmic information theory
Content Type	Text
Resource Type	Article
Subject	Mathematics Computer Science

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On the Computational Complexity of Small Descriptions

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Relativizations of the P-Printable Sets and the Sets with Small Generalized Kolmogorov Complexity (1992)

Lowness Properties of Sets in the Exponential-Time Hierarchy

SPARSE Reduces Conjunctively to TALLY

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On Tally Relativizations of $BP$-Complexity Classes

On Sets Truth-Table Reducible to Sparse Sets

With Quasilinear Queries EXP Is Not Polynomial Time Turing Reducible to Sparse Sets

Self-P-Printability and Polynomial Time Turing Equivalence to a Tally Set

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