文章基本信息

标题：DYNAMIC COMPLEXITY OF PARITY EXISTS QUERIES
本地全文：下载
作者：Nils Vortmeier ; Thomas Zeume
期刊名称：Logical Methods in Computer Science
印刷版ISSN：1860-5974
电子版ISSN：1860-5974
出版年度：2021
卷号：17
期号：4
页码：1-26
DOI：10.46298/lmcs-17(4:9)2021
语种：English
出版社：Technical University of Braunschweig
摘要：Given a graph whose nodes may be coloured red, the parity of the number of red nodes can easily be maintained with first-order update rules in the dynamic complexity framework DynFO of Patnaik and Immerman. Can this be generalised to other or even all queries that are definable in first-order logic extended by parity quantifiers? We consider the query that asks whether the number of nodes that have an edge to a red node is odd. Already this simple query of quantifier structure parity-exists is a major roadblock for dynamically capturing extensions of first-order logic. We show that this query cannot be maintained with quantifier-free first-order update rules, and that variants induce a hierarchy for such update rules with respect to the arity of the maintained auxiliary relations. Towards maintaining the query with full first-order update rules, it is shown that degree-restricted variants can be maintained.
关键词：Dynamic complexity;parity quantifier;arity hierarchy