1997 | Supplement | Chapter
Resource-Bounded Complexity
Authors : Ming Li, Paul Vitányi
Published in: An Introduction to Kolmogorov Complexity and Its Applications
Publisher: Springer New York
Included in: Professional Book Archive
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Recursion theory has a resource-bounded version in computational complexity theory. Similarly, Kolmogorov complexity has resource-bounded Kolmogorov complexity (also known as generalized Kolmogorov complexity). Several authors suggested early on the possibility of restricting the power of the device used to (de)compress strings. Says Kolmogorov:
“The concept discussed ...does not allow for the ‘difficulty’ of preparing a program
p
for passing from an object
x
to an object
y
. [... some] object permitting a very simple program, i.e., with very small complexity
K
(
x
) can be restored by short programs only as the result of computations of a thoroughly unreal nature. [... this concerns] the relationship between the necessary complexity of a program and its permissible difficulty
t
. The complexity
K
(
x
) that was obtained [before] is, in this case, the minimum of
K
t
(
x
) on the removal of the constraints on
t
.”