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arXiv · 2604.27939

Computing Witnesses Using the SCAN Algorithm

Fabian Achammer·Stefan Hetzl·Renate A. Schmidt
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Abstract

Second-order quantifier elimination is the problem of finding, given a formula with second-order quantifiers, a logically equivalent first-order formula. While such formulas are not computable in general, there are practical algorithms and subclasses with applications throughout computational logic. One of the most prominent algorithms for second-order quantifier elimination is the saturation-based SCAN algorithm. In this paper we show how the SCAN algorithm on clause sets can be extended to solve a more general problem: namely, finding a witness for the second-order quantifiers that results in a logically equivalent first-order formula. In addition, we provide a prototype implementation of the proposed method.

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Fabian Achammer, Stefan Hetzl, Renate A. Schmidt. 2026-04-30. Computing Witnesses Using the SCAN Algorithm. https://arxiv.org/abs/2604.27939

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