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arXiv · 1704.07998

A Strategy for Dynamic Programs: Start over and Muddle through

Samir Datta·Anish Mukherjee·Thomas Schwentick·Nils Vortmeier·Thomas Zeume
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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$^1$-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.

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Samir Datta, Anish Mukherjee, Thomas Schwentick, Nils Vortmeier, Thomas Zeume. 2017-04-26. A Strategy for Dynamic Programs: Start over and Muddle through. https://doi.org/10.23638/lmcs-15(2%3A12)2019

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