逻辑可约性与一元NP

S. Cosmadakis
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引用次数: 22

摘要

结果表明,通过选择适当的实例编码作为关系结构,可以在一阶逻辑中描述若干已知的多项式时间多一约简,并且它们是一元的。作为一个推论,证明了几个已知的一元NP中的NP完全问题不属于一元协同NP。进一步证明了即使有后继存在,从连通性到有向可达性也没有一元一阶约简。最后,证明了一些语法限制的一阶约简是不可比较的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Logical reducibility and monadic NP
It is shown that, by choosing appropriate encodings of instances as relational structures, several known polynomial-time many-one reductions can he described in first-order logic, and furthermore they are monadic. As a corollary, several known NP-complete problems in monadic NP are shown not to be in monadic co-NP. It is further shown that there is no monadic first-order reduction from connectivity to directed reachability, even in the presence of successor. Finally, some classes of syntactically restricted first-order reductions are shown to be incomparable.<>
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