技术控

    今日:118| 主题:49225
收藏本版 (1)
最新软件应用技术尽在掌握

[其他] Kolmogorov Complexity – A Primer – Math ∩ Programming

[复制链接]
巴黎铁塔的风景 发表于 2016-10-2 14:14:10
404 2

立即注册CoLaBug.com会员,免费获得投稿人的专业资料,享用更多功能,玩转个人品牌!

您需要 登录 才可以下载或查看,没有帐号?立即注册

x
The Complexity of Things

   Previously on this blog (quite a while ago), we’ve investigated some simple ideas of using randomness in artistic design ( psychedelic art , and earlier randomized css designs ), and measuring the complexity of such constructions . Here we intend to give a more thorough and rigorous introduction to the study of the complexity of strings. This naturally falls into the realm of computability theory and complexity theory, and so we refer the novice reader to our other primers on the subject ( Determinism and Finite Automata , Turing Machines , and Complexity Classes ; but Turing machines will be the most critical to this discussion).
  The Problem with Randomness

  What we would really love to do is be able to look at a string of binary digits and decide how “random” it is. On one hand, this is easy to do at a high level. A child would have no difficulty deciding which of the following two strings is more random:
   And yet, by the immutable laws of probability, each string has an equal chance (
Kolmogorov Complexity – A Primer – Math ∩ Programming-1 (difficulty,complexity,following,naturally,machines)
) in being chosen at random from all sequences of 50 binary digits. So in a sense, the huge body of mathematics underlying probability has already failed us at this basic juncture because we cannot speak of how random one particular outcome of an experiment is. We need a new notion that overcomes this difficulty.
   Definition: The Kolmogorov complexity of a string , denoted

Kolmogorov Complexity – A Primer – Math ∩ Programming-2 (difficulty,complexity,following,naturally,machines)
is the length of the shortest program which outputs given no input.
  While this definition is not rigorous enough to be of any use (we will reformulate it later), we can easily see why the first of the two strings above is less random. We can write a very short Python program that outputs it:
  [code]print "01" * 25[/code]  On the other hand, it is not hard to see that the shortest program that produces the second string is
  [code]print "00011101001000101101001000101111010100000100111101"[/code]  The dutiful reader will cry out in protest. How do you know that’s the shortest program? Why restrict to Python? This whole discussion is so arbitrary!
   Indeed, this is probably not the strictly shortest Python program that prints out the string. In the following we’ll work entirely in binary, so the picky reader should interpret this as a print command referring to a block of binary memory. We will reify these ideas in full rigor shortly, but first let us continue with this naivete to make the coming definitions a bit easier to parse.
   If we abstract away the lengths of these strings, we see that the length of the first program is
更多图片 小图 大图
组图打开中,请稍候......
友荐云推荐




上一篇:位换记号、排列测试与状态图:杂耍中的数学
下一篇:图表君聊Docker-images
酷辣虫提示酷辣虫禁止发表任何与中华人民共和国法律有抵触的内容!所有内容由用户发布,并不代表酷辣虫的观点,酷辣虫无法对用户发布内容真实性提供任何的保证,请自行验证并承担风险与后果。如您有版权、违规等问题,请通过"联系我们"或"违规举报"告知我们处理。

杨伟庆 发表于 2016-10-4 11:34:45
小白一个 顶一下
回复 支持 反对

使用道具 举报

与Hqァ偕佬 发表于 2016-11-14 12:11:05
巴黎铁塔的风景也是蛮拼的
回复 支持 反对

使用道具 举报

*滑动验证:
您需要登录后才可以回帖 登录 | 立即注册

本版积分规则

我要投稿

推荐阅读

扫码访问 @iTTTTT瑞翔 的微博
回页顶回复上一篇下一篇回列表手机版
手机版/CoLaBug.com ( 粤ICP备05003221号 | 文网文[2010]257号 )|网站地图 酷辣虫

© 2001-2016 Comsenz Inc. Design: Dean. DiscuzFans.

返回顶部 返回列表