Universal function: Difference between revisions
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LouScheffer (talk | contribs) Guidelines state one blue link per line, but on this subject more explanation seems helpful. |
Added (Levin's) universal one-way function. |
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A '''universal function''' is a function that can, in some defined way, imitate all other functions. |
A '''universal function''' is a function that can, in some defined way, imitate all other functions. This occurs in several contexts: |
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*In [[computer science]], a universal function is a [[computable function]] capable of calculating any other computable function. It is shown to exist by the [[utm theorem]]. |
*In [[computer science]], a universal function is a [[computable function]] capable of calculating any other computable function. It is shown to exist by the [[utm theorem]]. |
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*In [[cryptography]], a [[One-way_function#Universal_one-way_function|universal one-way function]] is a function that is known to be one-way if one-way functions exist. |
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*In [[mathematics]], a universal function is one that contains subregions that approximate every [[holomorphic function]] to arbitrary accuracy. The [[Riemann zeta function]] (and some others) have this property, as described in [[Zeta function universality]]. |
*In [[mathematics]], a universal function is one that contains subregions that approximate every [[holomorphic function]] to arbitrary accuracy. The [[Riemann zeta function]] (and some others) have this property, as described in [[Zeta function universality]]. |
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Revision as of 13:39, 24 February 2017
A universal function is a function that can, in some defined way, imitate all other functions. This occurs in several contexts:
- In computer science, a universal function is a computable function capable of calculating any other computable function. It is shown to exist by the utm theorem.
- In cryptography, a universal one-way function is a function that is known to be one-way if one-way functions exist.
- In mathematics, a universal function is one that contains subregions that approximate every holomorphic function to arbitrary accuracy. The Riemann zeta function (and some others) have this property, as described in Zeta function universality.