Joining Extractions of Regular Expressions

Regular expressions with capture variables, also knownas “regex formulas,” extract relations of spans (inter-val positions) from text. These relations can be fur-ther manipulated via Relational Algebra as studied inthe context of document spanners, Fagin et al.’s for-mal framework for information extraction. We investigate the complexity of querying text by ConjunctiveQueries (CQs) and Unions of CQs (UCQs) on top ofregex formulas. We show that the lower bounds (NP-completeness and W[1]-hardness) from the relationalworld also hold in our setting; in particular, hardnesshits already single-character text! Yet, the upper boundsfrom the relational world do not carry over. Unlike therelational world, acyclic CQs, and even gamma-acyclicCQs, are hard to compute. The source of hardness isthat it may be intractable to instantiate the relationdefined by a regex formula, simply because it has anexponential number of tuples. Yet, we are able to es-tablish general upper bounds. In particular, UCQs canbe evaluated with polynomial delay, provided that everyCQ has a bounded number of atoms (while unions andprojection can be arbitrary). Furthermore, UCQ evalu-ation is solvable with FPT (Fixed-Parameter Tractable)delay when the parameter is the size of the UCQ.