  We investigate the complexity of evaluating queries in Relational Algebra
(RA) over the relations extracted by regex formulas (i.e., regular expressions
with capture variables) over text documents. Such queries, also known as the
regular document spanners, were shown to have an evaluation with polynomial
delay for every positive RA expression (i.e., consisting of only natural joins,
projections and unions); here, the RA expression is fixed and the input
consists of both the regex formulas and the document. In this work, we explore
the implication of two fundamental generalizations. The first is adopting the
"schemaless" semantics for spanners, as proposed and studied by Maturana et al.
The second is going beyond the positive RA to allowing the difference operator.
We show that each of the two generalizations introduces computational hardness:
it is intractable to compute the natural join of two regex formulas under the
schemaless semantics, and the difference between two regex formulas under both
the ordinary and schemaless semantics. Nevertheless, we propose and analyze
syntactic constraints, on the RA expression and the regex formulas at hand,
such that the expressive power is fully preserved and, yet, evaluation can be
done with polynomial delay. Unlike the previous work on RA over regex formulas,
our technique is not (and provably cannot be) based on the static compilation
of regex formulas, but rather on an ad-hoc compilation into an automaton that
incorporates both the query and the document. This approach also allows us to
include black-box extractors in the RA expression.
