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Testing Satisfiability Asaf Shapira

Summary: Testing Satisfiability
Noga Alon
Asaf Shapira
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 k-SAT and k-NAEQ-SAT.
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


Source: Alon, Noga - School of Mathematical Sciences, Tel Aviv University


Collections: Mathematics