Dynamic Complexity under Definable Changes

DOI10.4230/LIPICS.ICDT.2017.19zbMATH Open1402.68051arXiv1701.02494OpenAlexW2904944004MaRDI QIDQ3174912

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Publication date: 18 July 2018

Abstract: 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) $A{C}^1$ 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 $Sigm{a}_1$-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.

Full work available at URL: https://arxiv.org/abs/1701.02494

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