Dynamic Complexity of Document Spanners

TL;DR

This paper explores the dynamic complexity of document spanners, demonstrating that regular spanners can be maintained efficiently in DynPROP, and that core spanners are maintainable in DynCQ and DynFO, advancing understanding of their computational properties.

Contribution

It establishes the dynamic complexity classes capable of maintaining various classes of document spanners, including regular, core, and generalized core spanners, using logical frameworks.

Findings

Regular spanners are maintainable in DynPROP.

Core spanners are maintainable in DynCQ.

Generalized core spanners are maintainable in DynFO.

Abstract

The present paper investigates the dynamic complexity of document spanners, a formal framework for information extraction introduced by Fagin, Kimelfeld, Reiss, and Vansummeren (JACM 2015). We first look at the class of regular spanners and prove that any regular spanner can be maintained in the dynamic complexity class DynPROP. This result follows from work done previously on the dynamic complexity of formal languages by Gelade, Marquardt, and Schwentick (TOCL 2012). To investigate core spanners we use SpLog, a concatenation logic that exactly captures core spanners. We show that the dynamic complexity class DynCQ, is more expressive than SpLog and therefore can maintain any core spanner. This result is then extended to show that DynFO can maintain any generalized core spanner and that DynFO is at least as powerful as SpLog with negation.