An Effective Characterization of the Alternation Hierarchy in Two-Variable Logic

被引：2
|
作者：
Krebs, Andreas [1 ]
Straubing, Howard [2 ]
机构：
[1] Univ Tubingen, Wilhelm Schickard Inst, Sand 13, D-72076 Tubingen, Germany
[2] Boston Coll, Comp Sci Dept, Chestnut Hill, MA 02467 USA
来源：
ACM TRANSACTIONS ON COMPUTATIONAL LOGIC | 2017年 / 18卷 / 04期
关键词：
FO2; Quantifier Alternation; J; Pseudovarities; Identities; CATEGORIES;
D O I：
10.1145/3149822
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
We give an algebraic characterization, based on the bilateral semidirect product of finite monoids, of the quantifier alternation hierarchy in two-variable first-order logic on finite words. As a consequence, we obtain a new proof that this hierarchy is strict. Moreover, by application of the theory of finite categories, we are able to make our characterization effective: that is, there is an algorithm for determining the exact quantifier alternation depth for a given language definable in two-variable logic.
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页数：22
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