Proper subclass status of REWB with positive/negative lookaheads relative to REWBLk

Determine whether regular expressions with backreferences and positive lookaheads (REWB with positive lookaheads) and regular expressions with backreferences and negative lookaheads (REWB with negative lookaheads) are proper subclasses of regular expressions with backreferences and lookaheads (REWBLk); specifically, prove or refute that both REWB with positive lookaheads and REWB with negative lookaheads are strictly contained in REWBLk rather than equal to it.

Background

The paper establishes that the class of languages definable by regular expressions with backreferences and lookaheads (REWBLk) coincides with NL and that its membership problem is PSPACE-complete. Earlier work had shown various inclusions and undecidability results for fragments, but the precise relationship between the lookahead-augmented fragments and the full REWBLk remained unsettled.

In the conclusion, the author explicitly notes that it remains unclear whether the two fragments—REWB with positive lookaheads and REWB with negative lookaheads—are proper subclasses of REWBLk, raising the question of strictness versus equality. Resolving this would clarify the role of positive and negative lookaheads (individually) in attaining the full power of REWBLk.