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@InProceedings{jha-fmcad16,
Author = {Susmit Jha and Vasumathi Raman and Sanjit A. Seshia},
Title = {On $\exists \forall \exists$ Solving: A Case Study on Automated Synthesis of Magic Card Tricks},
booktitle = {Proceedings of the IEEE International Conference on Formal Methods in Computer-Aided Design (FMCAD)},
month = "October",
year = {2016},
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 Exists-Forall-Exists 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.},
}