Complexity of Presburger arithmetic with fixed quantifier dimension

被引：18
|
作者：
Schöning U. [1 ]
机构：
[1] Abt. Theoretische Informatik, Universität Ulm
来源：
Theory of Computing Systems | 1997年 / 30卷 / 4期
关键词：
Decision Problem; Boolean Variable; Logical Theory; Universal Quantifier; Chinese Remainder Theorem;
D O I：
10.1007/BF02679468
中图分类号：
学科分类号：
摘要：
It is shown that the decision problem for formulas in Presburger arithmetic with quantifier prefix [∃1∀2 ⋯ ∃m∀3] (for m odd) and [∃1∀2 ⋯ ∀m∃3] (for m even) is complete for the class ΣPm of the polynomial-time hierarchy. Furthermore, the prefix type [∃∀∃∃] is complete for ΣP2, and the prefix type [∃∀] is complete for NP. This improves results (and solves a problem left open) by Grädel [7].
引用
收藏
页码：423 / 428
页数：5
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