Hard gaps in maximum constraint satisfaction problems? An equivalent formulation of PCP theorem is: For Max 3-SAT it is $NP$-hard to distinguish between satisfiable formulas and formulas where at most $r$-fraction of the clauses are satisfiable (for some $r\lt 1$). 


  Is there any known dichotomy theorem that classifies all Max CSP based on whether they have hard gaps or not?


Edit Dec 16, 2010: MAX CSP with hard gap means that the problem has optimal inapproximability factor. For instance, 3SAT has hard gap at location one since it is polynomial time approximable to a factor $7/8$ but it is $NP$-hard to obtain approximation factor $7/8+ \epsilon$ even when all clauses are satisfiable.
Prasad Raghavendra in the STOC'08 best paper proved a dichotomy conjecture for approximating Max-CSP assuming the Unique Games Conjecture. This is not how he presented it originally, but he did give talks presenting things this way a couple of years later, e.g., at the IAS, where it was videotaped:
http://www.math.ias.edu/seminars/abstract?event=36669

The difference from showing SNP-hardness is that here we talk about quantitatively optimal results.