Regular resolution is a refinement of the resolution proof system requiring that no variable be resolved on more than once along any path in the proof. It is known that there exist sequences of formulas that require exponential-size proofs in regular resolution while admitting polynomial-size proofs in resolution. Thus, with respect to the usual notion of simulation, regular resolution is separated from resolution. An alternative, and weaker, notion for comparing proof systems is that of an “effective simulation,” which allows the translation of the formula along with the proof when moving between proof systems. We prove that regular resolution is equivalent to resolution under effective simulations. As a corollary, we recover in a black-box fashion a recent result on the hardness of automating regular resolution.

中文翻译：

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常规分辨率有效模拟分辨率

常规解析是解析证明系统的改进，要求沿着证明中的任何路径对变量进行多次解析。众所周知，存在需要常规分辨率下的指数大小证明，同时在分辨率上允许多项式大小证明的公式序列。因此，对于通常的模拟概念，常规分辨率与分辨率是分开的。比较证明系统的另一种较弱的概念是“有效模拟”，它允许在证明系统之间移动时随证明一起翻译公式。我们证明常规分辨率与有效模拟下的分辨率等效。作为推论，我们以黑盒方式恢复了有关自动化常规解析难度的最新结果。