File:Kolmogorov complexity and computable lower bounds.gif
Summary
Shows the <a href="https://en.wikipedia.org/wiki/Kolmogorov_complexity" class="extiw" title="en:Kolmogorov complexity">Kolmogorov complexity</a> K(s) (red), and two computable lower bound functions prog1(s) (yellow), prog2(s) (green). The horizontal axis (<a href="https://en.wikipedia.org/wiki/logarithmic_scale" class="extiw" title="en:logarithmic scale">logarithmic scale</a>) enumerates all <a href="https://en.wikipedia.org/wiki/string_(computer_science)" class="extiw" title="en:string (computer science)">strings</a> s, ordered by length; the vertical axis (<a href="https://en.wikipedia.org/wiki/linear_scale" class="extiw" title="en:linear scale">linear scale</a>) measures string length in <a href="https://en.wikipedia.org/wiki/bit" class="extiw" title="en:bit">bits</a>. Most strings are incompressible, i.e. their Kolmogorov complexity exceeds their length by a constant amount. 17 compressible strings are shown in the picture, appearing as almost vertical slopes. Due to <a href="https://en.wikipedia.org/wiki/Kolmogorov_complexity#Chaitin.27s_incompleteness_theorem" class="extiw" title="en:Kolmogorov complexity">Chaitin's incompleteness theorem</a>, the output of any program computing a lower bound of the Kolmogorov complexity cannot exceed some fixed limit, which is independent of the input string s.
Licensing
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File history
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 17:39, 5 January 2017 | | 1,000 × 293 (4 KB) | 127.0.0.1 (talk) | Shows the <a href="https://en.wikipedia.org/wiki/Kolmogorov_complexity" class="extiw" title="en:Kolmogorov complexity">Kolmogorov complexity</a> <i>K</i>(<i>s</i>) <span style="background:transparent;color: #c00000;" title="transparent">(red)</span>, and two computable lower bound functions <code>prog1(s)</code> <span style="background:transparent;color: #c0c000;" title="transparent">(yellow)</span>, <code>prog2(s)</code> <span style="background:transparent;color: #00c000;" title="transparent">(green)</span>. The horizontal axis (<a href="https://en.wikipedia.org/wiki/logarithmic_scale" class="extiw" title="en:logarithmic scale">logarithmic scale</a>) enumerates all <a href="https://en.wikipedia.org/wiki/string_(computer_science)" class="extiw" title="en:string (computer science)">strings</a> <i>s</i>, ordered by length; the vertical axis (<a href="https://en.wikipedia.org/wiki/linear_scale" class="extiw" title="en:linear scale">linear scale</a>) measures string length in <a href="https://en.wikipedia.org/wiki/bit" class="extiw" title="en:bit">bits</a>. Most strings are incompressible, i.e. their Kolmogorov complexity exceeds their length by a constant amount. 17 compressible strings are shown in the picture, appearing as almost vertical slopes. Due to <a href="https://en.wikipedia.org/wiki/Kolmogorov_complexity#Chaitin.27s_incompleteness_theorem" class="extiw" title="en:Kolmogorov complexity">Chaitin's incompleteness theorem</a>, the output of any program computing a lower bound of the Kolmogorov complexity cannot exceed some fixed limit, which is independent of the input string <i>s</i>. |
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