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arXiv · 2412.10066

Non-Ground Congruence Closure

Hendrik Leidinger·Christoph Weidenbach
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Abstract

Congruence closure on ground equations is a well-established and efficient algorithm for deciding ground equalities. It constructs an explicit representation of ground equivalence classes based on a given set of input equations, allowing ground equalities to be decided by membership. In many applications, these ground equations originate from grounding non-ground equations. We propose an algorithm that directly computes a non-ground representation of ground congruence classes for non-ground equations. Our approach is sound and complete with respect to the corresponding ground congruence classes. Experimental results demonstrate that computing non-ground congruence classes often outperforms the classical ground congruence closure algorithm in efficiency.

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Hendrik Leidinger, Christoph Weidenbach. 2024-12-13. Non-Ground Congruence Closure. https://arxiv.org/abs/2412.10066

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