 
Summary: Testing Satisfiability
Noga Alon
Asaf Shapira
Abstract
Let be a set of general boolean functions on n
variables, such that each function depends on exactly
k variables, and each variable can take a value from
[1, d]. We say that is far from satisfiable, if one
must remove at least nk
functions in order to make
the set of remaining functions satisfiable. Our main
result is that if is far from satisfiable, then most
of the induced sets of functions, on sets of variables
of size c(k, d)/ 2
, are not satisfiable, where c(k, d)
depends only on k and d. Using the above claim, we
obtain similar results for kSAT and kNAEQSAT.
Assume we relax the decision problem of whether
an instance of one of the above mentioned problems is
satisfiable or not, to the problem of deciding whether
