浅谈复杂度理论中的归约(Reduction) - 知乎 - 知乎专栏
网页众所周知，“归约”（Reduction）在计算复杂度理论中是一个非常重要的概念。 \mathsf {NP} -Complete 等复杂度类的定义就离不开这个概念。 本文会用几个例子介绍一下归约的基本定义，不同种类的归约，以及讲几个笑话。 那我们先从一个古老的笑话开始： 一个物理学家和一个数学家正坐在教师休息室里。 突然间，休息室里的咖啡机着火了。 物理学家就拿了一个垃圾桶，把里面的垃圾清空，跑到水池前，给垃圾桶灌满水，随后扑灭了火。 由于这个咖 …
Lecture 9: Reducibility | Theory of Computation | Mathematics
网页Discussed the reducibility method to prove undecidability and T-unrecognizability. Defined mapping reducibility as a type of reducibility. Showed that E T M is undecidable and T-unrecognizable; E Q T M and E Q T M ― are T-unrecognizable. …
网页Reducibility – Concept. If we have two languages (or problems) ! and ", then ! is reducible to " means that we can use " to solve !. Example 1: Measuring the area of a rectangle is reducible to measuring the lengths of its sides. Example 2: We showed that !NFA is reducible to !DFA .
网页What is reducibility? A reduction is a way of converting one problem to another, such that the solution to the second can be used to solve the first. We say that problem A is reducible to problem B. Example: Finding your way around New York City is reducible to the problem of finding and reading a map.
网页A reduction from A to. : Σ 1* → Σ 2* such that. is a function. For any w ∈ Σ 1*, w ∈ A.
网页What is Reducibility? A reduction is a way of converting one problem to another such that the solution to the second can be used to solve the first – We say that problem A is reducible to problem B – If A reduces to B, what can we say about the relative difficulty of …
网页So today, as I mentioned, we're going to talk about the reducibility method for proving problems undecidable and also for proving problems non-turing recognizable, Turing unrecognizable. We're going to introduce this notion of a reducibility in general. And we'll also talk about a very specific kind of reducibility called the mapping reducibility.
网页Mapping reducibility A language is mapping reducible to (write ) if there exists a computable function such that for every That is, the function !maps members of A to members of B and non-members of A to non-members of B • Example: .
网页Mapping reducibility (today / Monday), and Polynomial-time reducibility (next week).
网页•reducibility helps in classifying problems by decidability •when A is reducible to B, solving A cannot be harder than solving B because a solution to B gives a solution to A •if A is reducible to B and B is decidable, then A is also decidable •if A is undecidable and reducible to B, then B is undecidable
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