J. Balc'azar and R. Book. Sets with small generalized Kolmogorov complexity. Acta Informatica, 23(6):679--688, 1986. Home/Search Document Not in Database Summary Related Articles Check |
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Lower Bounds for the Low Hierarchy - Allender, Hemachandra (27 citations) (Correct)
....low hierarchies. In some cases, we are able to improve known lowness results. More importantly, we present the first theorems showing that various lowness results cannot be improved. For example, we show the existence of a sparse set that is not in EL 2 , thus answering a question posed in [BB 86]. Although we are able to construct sets that are not in certain levels of the extended low hierarchy, we cannot hope to prove similar results for the low hierarchy within NP, unless wearefirstabletoproveP#=NP. Given that that is beyond current techniques, the best that we can do is to construct ....
....# .Notealso that A # NP. 7 algorithm for recognizing A is as follows. On input x,constructt an encoding of the strings in A of length i by determining if 0 T # for 0 i. Then accept x x, t##A # (which can be determined by one call to SAT) Corollary 9 ET (TALLY ) EL 2 . [BB 86] Left cuts of real numbers were introduced into complexity theory by Ko [Ko 82] Ko defined standard left cuts and general left cuts. Lowness results are known for both. Selman showed that every Standard Left Cut is in ET (TALLY ) Se 81] we improve this below to show that every General Left Cut ....
J. Balcazar and R. Book, Sets with small generalized Kolmogorov complexity, Acta Informatica 23, 679--688.
L-Printable Sets - Fortnow, Goldsmith, Levy, Mahaney (1996) (1 citation) (Correct)
....1 A set is said to have small generalized Kolmogorov complexity if all of its strings are highly compressible and easily restorable. Generalized time bounded Kolmogorov complexity and generalized space bounded Kolmogorov complexity are introduced in [Ha83] and [S83] Several researchers [R86, BB86, HH88] show that P printable sets are exactly the sets in P with small generalized time bounded Kolmogorov complexity. AR88] show that a set has small generalized time bounded Kolmogorov complexity if and only if it is P isomorphic to a tally set. Using similar techniques, we show in Section 5 that the ....
....is, we recompute M u (x) and print out the result. The entire computation only needs O(log n) space, so S is L printable. 2 It was shown in [AR88] that a set has small generalized Kolmogorov complexity if and only it is P isomorphic to a tally set. Note: this was improvement of the result in [BB86], which showed that a set has small generalized Kolmogorov complexity if and only if it is semi isomorphic to a tally set. Using a similar argument and Theorem 27 we can show an analogous result for sets with small generalized Kolmogorov space complexity. First, we prove the following result. ....
J. Balcazar and R. Book. Sets with Small Generalized Kolmogorov Complexity. Acta Informatica, 23:679--688, 1986.
L-Printable Sets - Fortnow, Goldsmith, Levy, Mahaney (1999) (1 citation) (Correct)
....A set is said to have small generalized Kolmogorov complexity if all of its strings are highly compressible and easily restorable. Generalized time bounded Kolmogorov complexity and generalized space bounded Kolmogorov complexity are introduced in [Har83] and [Sip83] Several researchers [Rub86, BB86, HH88] show that P printable sets are exactly the sets in P with small generalized time bounded Kolmogorov complexity. AR88] show that a set has small generalized time bounded Kolmogorov complexity if and only if it is P isomorphic to a tally set. Using similar techniques, we show in x 5 that the ....
....it is, we recompute M u (x) and print out the result. The entire computation only needs O(log n) space, so S is L printable. It was shown in [AR88] that a set has small generalized Kolmogorov complexity if and only it is P isomorphic to a tally set. Note: this was improvement of the result in [BB86], which showed that a set has small generalized Kolmogorov complexity if and only if it is semi isomorphic to a tally set. Using a similar argument and Theorem 5.2 we can show an analogous result for sets with small generalized Kolmogorov space complexity. First, we prove the following result. ....
J. Balcazar and R. Book, Sets with small generalized Kolmogorov complexity, Acta Inform., 23 (1986), pp. 679--688.
Polynomial-Time Semi-Rankable Sets - Lane Hemaspaandra Mohammed (1995) (Correct)
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J. Balc'azar and R. Book. Sets with small generalized Kolmogorov complexity. Acta Informatica, 23(6):679--688, 1986.
Scaled dimension and the Kolmogorov complexity of.. - Hitchcock.. (Correct)
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J. L. Balcazar and R. V. Book. Sets with small generalized Kolmogorov complexity. Acta Informatica, 23:679--688, 1986. 22
Almost Everywhere High Nonuniform Complexity - Lutz (1992) (99 citations) (Correct)
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J.L. Balc'azar and R.V. Book, Sets with small generalized Kolmogorov complexity, Acta Informatica 23 (1986), pp. 679--688.
Circuit Size Relative to Pseudorandom Oracles - Lutz, Schmidt (1993) (10 citations) (Correct)
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J. L. Balc'azar and R. V. Book, Sets with small generalized Kolmogorov complexity, Acta Informatica 23 (1986), pp. 679--688.
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