AI笔记 The SAT problem

最新推荐文章于 2023-02-09 20:08:14 发布

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最新推荐文章于 2023-02-09 20:08:14 发布 · 2.7k 阅读

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#SAT #ai

本文探讨了婚礼座位安排问题，将其转化为经典的SAT问题。介绍了SAT问题的定义，涉及地图涂色和理事会等问题，并讲解了DPLL算法的工作原理，包括将问题转化为CNF形式，通过假设检验判断解决方案的可行性。文章最后指出该算法的效率问题及其时间复杂度。

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The problems

Suppose you have a wedding to plan, and want to arrange the wedding seating for a certain number of guests in a hall. The hall has a certian number of tables for seating. Some pairs of guests are couples or close Friends(F) and want to sit together at the same table. Some other pairs of guestes are Enemies(E) and want to sit together at the same table. The rest of the pairs are Indifferent(I) to each other and do not mind sitting together or not. However, each pair of guests can have ONLY one relationship, (E), (F) or (I). Find a seating arrangement that satisfies the constrains.

SAT问题即满足问题。给定一个规则(约束条件)和dataset(数据集)，求证这个数据集能否满足这个规则，如果满足，给出可能的解。历史上有很多经典SAT问题，例如地图涂色问题，婚礼问题，理事会问题。

DPLL是解此类问题的一个经典算法，DPLL是4个算法发明人名字的首字母。这四个人是Martin Davis, Hilary Putnam, George Logemann, and Donal