Feasible interpolation is a general technique for proving proof complexity lower bounds. The monotone version of the technique converts, in its basic variant, lower bounds for monotone Boolean circuits separating two NP-sets to proof complexity lower bounds. In a generalized version of the technique, dag-like communication protocols are used instead of monotone Boolean circuits. We study three kinds of protocols and compare their strength. Our results establish the following relationships in the sense of polynomial reducibility: Protocols with equality are at least as strong as protocols with inequality and protocols with equality have the same strength as protocols with a conjunction of two inequalities. Exponential lower bounds for protocols with inequality are known. Obtaining lower bounds for protocols with equality would immediately imply lower bounds for resolution with parities (R(LIN)).
翻译:简单技术的单质版本在其基本变式中,将单质波伦电路的下限转换为单质波列安电路的下限,将两套NP-套件分开,以证明复杂性的下限。在这种技术的通用版本中,使用类似达格的通信协议,而不是单质波列安电路。我们研究三种协议并比较其强度。我们的结果在多元可复制性意义上确立了以下关系:平等议定书至少与不平等议定书和平等议定书具有与两种不平等相结合的相同强度。不平等协议的上下限是已知的。获得平等协议的下限将立即意味着与平等性协议的下限(R(LIN) )。