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arXiv · 2309.01750

On CNF formulas irredundant with respect to unit clause propagation

Petr Savický
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Abstract

Two CNF formulas are called ucp-equivalent, if they behave in the same way with respect to the unit clause propagation (UCP). A formula is called ucp-irredundant, if removing any clause leads to a formula which is not ucp-equivalent to the original one. As a consequence of known results, the ratio of the size of a ucp-irredundant formula and the size of a smallest ucp-equivalent formula is at most $n^2$, where $n$ is the number of the variables. We demonstrate an example of a ucp-irredundant formula for a symmetric definite Horn function which is larger than a smallest ucp-equivalent formula by a factor $Ω(n/\ln n)$. Consequently, a general upper bound on the above ratio cannot be smaller than this.

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Petr Savický. 2025-06-27. On CNF formulas irredundant with respect to unit clause propagation. https://arxiv.org/abs/2309.01750

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