Irreducible Hamiltonian BRST - anti-BRST formalism for off-shell reducible theories

In this paper with develop an irreducible Hamiltonian BRST - anti-BRST symmetry for off-shell reducible theories. Our procedure consists in deriving an irreducible theory associated with the original reducible one such that the physical observables corresponding to the two systems coincide. The possibility to construct an irreducible BRST - anti-BRST symmetry (related to the irreducible system) together with the equivalence between the physical observables ensure, on behalf of the fundamental equations of the BRST - anti-BRST formalism, that it is permissible to substitute the BRST - anti-BRST symmetry of the reducible theory by that of the irreducible system. The general procedure is illustrate on two-form gauge fields. (authors)