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It is shown that languages definable by weak pebble automata are not closed under reversal. For the proof, we establish a kind of periodicity of an automaton’s computation over a specific set of words. The periodicity is partly due to the finiteness of the automaton description and partly due to the word’s structure. Using such a periodicity we can find a word such that during the automaton’s run on it there are two different, yet indistinguishable, configurations. This enables us to remove a part of that word without affecting acceptance. Choosing an appropriate language leads us to the desired result.

Regular expressions with capture variables, also known as "regex formulas,'' extract relations of spans (interval positions) from text. These relations can be further manipulated via the relational Algebra as studied in the context of "document spanners," Fagin et al.'s formal framework for information extraction. We investigate the complexity of querying text by Conjunctive Queries (CQs) and Unions of CQs (UCQs) on top of regex formulas. Such queries have been investigated in prior work on document spanners, but little is known about the (combined) complexity of their evaluation. We show that the lower bounds (NP-completeness and W[1]-hardness) from the relational world also hold in our setting; in particular, hardness hits already single-character text. Yet, the upper bounds from the relational world do not carry over. Unlike the relational world, acyclic CQs, and even gamma-acyclic CQs, are hard to compute. The source of hardness is that it may be intractable to instantiate the relation defined by a regex formula, simply because it has an exponential number of tuples. Yet, we are able to establish general upper bounds. In particular, UCQs can be evaluated with polynomial delay, provided that every CQ has a bounded number of atoms (while unions and projection can be arbitrary). Furthermore, UCQ evaluation is solvable with FPT (Fixed-Parameter Tractable) delay when the parameter is the size of the UCQ.

Modern information extraction pipelines are typically constructed by (1) loading textual data from a database into a special-purpose application, (2) applying a myriad of text-analytics functions to the text, which produce a structured relational table, and (3) storing this table in a database. Obviously, this approach can lead to laborious development processes, complex and tangled programs, and inefficient control flows. Towards solving these deficiencies, we embark on an effort to lay the foundations of a new generation of text-centric database management systems. Concretely, we extend the relational model by incorporating into it the theory of document spanners which provides the means and methods for the model to engage the Information Extraction (IE) tasks. This extended model, called Spannerlog, provides a novel declarative method for defining and manipulating textual data, which makes possible the automation of the typical work method described above. In addition to formally defining Spannerlog and illustrating its usefulness for IE tasks, we also report on initial results concerning its expressive power.