Abstract
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 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.” [Kolmogorov]
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© 1993 Springer Science+Business Media New York
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Li, M., Vitányi, P. (1993). Resource-Bounded Complexity. In: An Introduction to Kolmogorov Complexity and Its Applications. Texts and Monographs in Computer Science. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-3860-5_7
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DOI: https://doi.org/10.1007/978-1-4757-3860-5_7
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4757-3862-9
Online ISBN: 978-1-4757-3860-5
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