2017/01/10 by Thomas Schwentick, Schwentick, Thomas, Nils Vortmeier +3
Computer Science · #Computability, Logic, AI Algorithms #Databases (cs.DB) #Distributed systems and fault tolerance #F.4.1 #FOS: Computer and information sciences #Logic in Computer Science (cs.LO) #Logic, programming, and type systems #cs.DB #cs.LO
paper · pdf · doi:10.48550/arxiv.1701.02494
Full version of an article to be published in ICDT 2017
arxiv created 2017/01/10 · openalex publication_date 2017/01/10 · arxiv updated 2017/01/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper studies dynamic complexity under definable change operations in the DynFO framework by Patnaik and Immerman. It is shown that for changes definable by parameter-free first-order formulas, all (uniform) AC1 queries can be maintained by first-order dynamic programs. Furthermore, many maintenance results for single-tuple changes are extended to more powerful change operations: (1) The reachability query for undirected graphs is first-order maintainable under single tuple changes and first-order defined insertions, likewise the reachability query for directed acyclic graphs under quantifier-free insertions. (2) Context-free languages are first-order maintainable under Σ1-defined changes. These results are complemented by several inexpressibility results, for example, that the reachability query cannot be maintained by quantifier-free programs under definable, quantifier-free deletions.