二阶布尔逻辑Horn和Krom片断的复杂性
On the Complexity of Horn and Krom Fragments of Second-Order Boolean Logic
摘要：
二阶布尔逻辑是QBF的推广，其常数交替片段已知对于指数时间层次的水平是完全的。我们考虑这种逻辑的两种类型的限制：1）对项构造的限制，2）对布尔矩阵的形式的限制。对于第一类，我们考虑两种限制：首先，不允许嵌套使用适当的函数变量，其次规定每个函数变量必须以固定的参数序列出现。第二种，我们考虑霍恩，克罗姆，和核心片段的布尔矩阵。我们分类的复杂性的逻辑得到这两种类型的限制相结合。我们表明，在大多数情况下，逻辑与k交替块的函数量词是完整的指数时间层次的第k或（k-1）级。此外，我们建立NL-完全的克罗姆和核心片段，当k=1和第一类的限制都有效。
英文摘要：
Second-order Boolean logic is a generalization of QBF, whose constant alternation fragments are known to be complete for the levels of the exponential time hierarchy. We consider two types of restriction of this logic: 1) restrictions to term constructions, 2) restrictions to the form of the Boolean matrix. Of the first sort, we consider two kinds of restrictions: firstly, disallowing nested use of proper function variables, and secondly stipulating that each function variable must appear with a fixed sequence of arguments. Of the second sort, we consider Horn, Krom, and core fragments of the Boolean matrix. We classify the complexity of logics obtained by combining these two types of restrictions. We show that, in most cases, logics with k alternating blocks of function quantifiers are complete for the kth or (k-1)th level of the exponential time hierarchy. Furthermore, we establish NL-completeness for the Krom and core fragments, when k=1 and both restrictions of the first sort are in effect.
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