On ∃ ∀ ∃! solving: A case study on automated synthesis of magic card tricks

2016 Formal Methods in Computer-Aided Design (FMCAD) Pub Date : 2016-10-03 DOI:10.1109/FMCAD.2016.7886664

Susmit Jha, Vasumathi Raman, S. Seshia

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引用次数: 1

Abstract

In formal synthesis, the goal is to find a composition of components from a finite library such that the composition satisfies a given logical specification. In this paper, we consider the problem of synthesizing magic card tricks from component actions, where some of the actions depend on non-deterministic choices made by the audience. This problem can be naturally represented as a quantified logical formula of the form: Exists a composition, Forall nondeterministic choices, Uniquely-Exists intermediate and final outputs satisfying a logical specification, that is, an (∃∀∃!) satisfiability problem. We present a novel approach to solve this problem that exploits the unique-existence of intermediate and final outputs for any given composition and choice values. We illustrate how several popular magic card tricks can be recovered using this approach. These tricks evolved through human ingenuity over decades, but we demonstrate that formal synthesis can generate a number of novel variants of these tricks within minutes. In contrast, a direct encoding to quantified SMT problem fails to find a solution in hours.

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∃∀!解决:一个自动合成魔术卡片技巧的案例研究

在形式合成中，目标是从有限的库中找到组件的组合，使该组合满足给定的逻辑规范。在本文中，我们考虑了由组成动作合成魔术牌技巧的问题，其中一些动作依赖于观众所做的不确定性选择。这个问题可以自然地表示为一个量化的逻辑公式:存在一个组合，对于所有不确定的选择，唯一存在满足逻辑规范的中间和最终输出，即一个(∃∀∃!)可满足性问题。我们提出了一种新的方法来解决这个问题，利用中间和最终输出的唯一存在对于任何给定的组成和选择值。我们将说明如何使用这种方法恢复几种流行的魔术卡片技巧。这些把戏经过人类几十年的聪明才智进化而来，但我们证明，正式合成可以在几分钟内产生许多这些把戏的新变体。相比之下，直接编码量化SMT问题无法在数小时内找到解决方案。

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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2016 Formal Methods in Computer-Aided Design (FMCAD)

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