  The celebrated Curci-Ferrari (CF) type of restrictions are invoked to obtain
the off-shell nilpotent and absolutely anticommuting (anti-) BRST as well as
(anti-) co-BRST symmetry transformations in the context of the Lagrangian
description of the physical four (3 + 1)-dimensional (4D) free Abelian 2-form
gauge theory. We show that the above CF type conditions, which turn out to be
the secondary constraints of the theory, remain invariant with respect to the
time-evolution of the above 2-form gauge system in the Hamiltonian formulation.
This time-evolution invariance (i) physically ensures the linear independence
of the BRST versus anti-BRST as well as co-BRST versus anti-co-BRST symmetry
transformations, and (ii) provides a logical reason behind the imposition of
the above CF type restrictions in the proof of the absolute anticommutativity
of the off-shell nilpotent (anti-) BRST as well as (anti-) co-BRST symmetry
transformations.
