泛一阶逻辑是NL、P、NP和coNP的超逻辑
Universal First-Order Logic is Superfluous for NL, P, NP and coNP
摘要：
在这项工作中，我们继续的句法研究的完整性，开始与工程Immerman和麦地那。特别是，我们采取了梅迪纳在他的论文中提出的一个猜想，即如果一个二阶和一阶句子的连接通过fops定义了一个NP完全问题，那么它必须是这样的情况下，二阶连接单独也定义了一个NP完全问题。虽然这个主张看起来非常合理和直观，但目前我们还不能提供一个明确的答案。然而，我们可以肯定地解决一个较弱的主张，即所有“一致”的普遍一阶句都可以安全地消除，而不必担心失去完整性。我们的方法是相当普遍的，可以适用于复杂性类以外的NP（在本文中：NLSPACE，PTIME，和coNP），提供类有一个完整的问题，满足一定的组合属性。
英文摘要：
In this work we continue the syntactic study of completeness that began with the works of Immerman and Medina. In particular, we take a conjecture raised by Medina in his dissertation that says if a conjunction of a second-order and a first-order sentences defines an NP-complete problems via fops, then it must be the case that the second-order conjoint alone also defines a NP-complete problem. Although this claim looks very plausible and intuitive, currently we cannot provide a definite answer for it. However, we can solve in the affirmative a weaker claim that says that all ``consistent'' universal first-order sentences can be safely eliminated without the fear of losing completeness. Our methods are quite general and can be applied to complexity classes other than NP (in this paper: to NLSPACE, PTIME, and coNP), provided the class has a complete problem satisfying a certain combinatorial property.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
