Capturing complexity classes by fragments of second order logic

[1991] Proceedings of the Sixth Annual Structure in Complexity Theory Conference Pub Date : 1900-01-01 DOI:10.1109/SCT.1991.160279

E. Gradel

引用次数: 1

Abstract

The expressive power of certain fragments of second-order logic on finite structures is investigated. The fragments are second-order Horn logic, second-order Krom logic, and a symmetric and a deterministic version of the latter. It is shown that all these logics collapse to their existential fragments. In the presence of a successor relation they provide characterizations of polynomial time, deterministic and nondeterministic logspace and of the complement of symmetric logspace. Without a successor relation these logics can still express certain problems that are complete in the corresponding complexity classes, but they are strictly weaker than previously known logics for these classes and fail to express some very simple properties.<>

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通过二阶逻辑片段捕获复杂度类

研究了二阶逻辑片段在有限结构上的表达能力。这些片段是二阶霍恩逻辑、二阶克罗姆逻辑以及后者的对称和确定性版本。结果表明，所有这些逻辑都瓦解为它们存在的碎片。在后继关系的存在下，给出了多项式时间、确定性和非确定性对数空间以及对称对数空间的补的刻画。在没有后继关系的情况下，这些逻辑仍然可以表达在相应的复杂性类中完整的某些问题，但它们比这些类的先前已知逻辑严格弱，并且无法表达一些非常简单的性质

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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[1991] Proceedings of the Sixth Annual Structure in Complexity Theory Conference

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