Using a SAT Solver to Find Interesting Sets of Nonstandard Dice

IF 0.4 4区数学 Q4 MATHEMATICS American Mathematical Monthly Pub Date : 2023-02-22 DOI:10.1080/00029890.2023.2178218

Michael Purcell

引用次数: 1

Abstract

Abstract We describe a family of Boolean satisfiability (SAT) problems for which each solution corresponds to a unique set of nonstandard dice. We show that we can control the relationships between the dice in each solution by imposing a set of cardinality constraints on the variables in the corresponding SAT problem. We then present examples of interesting sets of nonstandard dice that we found by solving such problems. In particular, we describe a set of 19 five-sided dice that realize the Paley tournament on 19 vertices. Furthermore, we show that this set of dice is minimal in the sense that no set of 19 dice with less than five sides can realize the Paley tournament on 19 vertices.

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使用SAT解算器查找有趣的非标准骰子集

摘要我们描述了一类布尔可满足性（SAT）问题，其每个解对应于一组唯一的非标准骰子。我们证明，我们可以通过对相应SAT问题中的变量施加一组基数约束来控制每个解决方案中骰子之间的关系。然后，我们给出了一些有趣的非标准骰子集的例子，这些骰子是我们通过解决这些问题而发现的。特别地，我们描述了一组19个五边骰子，它们在19个顶点上实现了Paley锦标赛。此外，我们证明了这组骰子是最小的，因为没有一组边小于5的19个骰子可以在19个顶点上实现Paley锦标赛。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

American Mathematical Monthly Mathematics-General Mathematics

CiteScore

0.80

自引率

20.00%

发文量

127

审稿时长

6-12 weeks

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