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cover of episode Episode 10: What Use is Computational Theory?

Episode 10: What Use is Computational Theory?

2020/12/20
logo of podcast The Theory of Anything

The Theory of Anything
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Bruce: 本集探讨了计算理论在现实生活中的应用，例如理解算法的速度和可计算性。首先，通过分析冒泡排序算法，解释了算法复杂度（Big O notation）的概念，并说明了如何评估算法的运行时间。然后，介绍了算法的复杂度类，包括线性时间、多项式时间和指数时间，并指出指数时间算法的不可处理性。Bruce还讨论了NP完全问题，解释了其普遍性以及寻找多项式时间算法的难度。最后，他介绍了不可计算性（undecidability）的概念，并以图灵停机问题为例，说明了某些问题的不可计算性。他还讨论了量子计算机及其对计算理论的影响，特别是Shor算法如何解决当前加密算法中的难题。 Cameo: Cameo主要参与讨论，提出问题，并对Bruce的解释进行回应。她对算法复杂度、NP完全问题和不可计算性的概念表示理解，并参与了关于这些概念的讨论。Cameo还表达了对人工智能和软件开发中计算理论应用的兴趣，并提出了一些相关的问题。

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The episode introduces computational theory and its practical applications, focusing on how it is used in real-life scenarios such as programming and algorithm development.

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In the last episode, we gave you the basic theory. Now we're going to show you how Computational Theory is actually used in real life. We'll discuss the various computational classes that exist and one special class in particular: NP-Complete. Using reducibility (as discussed in the previous episode) we can prove that this is a universal class of problems. This provides us evidence (but not a proof!) that many algorithms are too slow to be tractable (i.e. return a result in a useful amount of time.) Finally, we'll discuss the startling fact that some problems can't be computed at all because the laws of physics don't allow it.

Youtube version with optional visuals:

https://www.youtube.com/watch?v=rVpM8XOwmz4

Note: Due to the nature of these Computational theory episodes, it might be helpful to see the Youtube visuals.

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