We define instance compressibility for parametric problems in PH and PSPACE. We observe that

the problem \Sigma_{i}CircuitSAT of deciding satisfiability of a quantified Boolean circuit with i-1 alternations of quantifiers starting with an existential uantifier is complete for parametric problems in \Sigma_{i}^{p} with respect to W-reductions, and that analogously the problem QBCSAT (Quantified Boolean Circuit Satisfiability) is complete for parametric problems in PSPACE with respect to W-reductions. We show the following results about these problems:

1) If CircuitSAT is non-uniformly compressible within NP, then \Sigma_{i}CircuitSAT is non-uniformly compressible within NP, for any i >= 1.

2) If QBCSAT is non-uniformly compressible (or even if satisfiability of quantified Boolean CNF formulae is non-uniformly compressible), then PSPACE is contained in NP/poly and PH collapses to the third level.

Next, we define Succinct Interactive Proof (Succinct IP) and scrutinizing the proof of IP = PSPACE, we show that QBFormulaSAT (Quantified Boolean Formula Satisfiability) is in Succinct IP. On the contrary if QBFormulaSAT has Succinct PCPs, Polynomial Hierarchy (PH) collapses.