  In [GH1] and [GH2] (see also [GH3]) we presented full proof of the equalities
NP = coNP = PSPACE. These results have been obtained by the novel proof
theoretic tree-to-dag compressing techniques adapted to Prawitz's Natural
Deduction (ND) for propositional minimal logic coupled with the corresponding
Hudelmaier's cutfree sequent calculus. In this paper we propose an overview of
our proofs.
