A Strategy for Dynamic Programs: Start over and Muddle through
Abstract
In the setting of DynFO, dynamic programs update the stored result of a query whenever the underlying data changes. This update is expressed in terms of first-order logic. We introduce a strategy for constructing dynamic programs that utilises periodic computation of auxiliary data from scratch and the ability to maintain a query for a limited number of change steps. We show that if some program can maintain a query for log n change steps after an AC-computable initialisation, it can be maintained by a first-order dynamic program as well, i.e., in DynFO. As an application, it is shown that decision and optimisation problems defined by monadic second-order (MSO) formulas are in DynFO, if only change sequences that produce graphs of bounded treewidth are allowed. To establish this result, a Feferman-Vaught-type composition theorem for MSO is established that might be useful in its own right.
Cite
@article{arxiv.1704.07998,
title = {A Strategy for Dynamic Programs: Start over and Muddle through},
author = {Samir Datta and Anish Mukherjee and Thomas Schwentick and Nils Vortmeier and Thomas Zeume},
journal= {arXiv preprint arXiv:1704.07998},
year = {2023}
}