Hardness Results for Approximate Pure Horn CNF Formulae Minimization

04/16/2012
by   Endre Boros, et al.
0

We study the hardness of approximation of clause minimum and literal minimum representations of pure Horn functions in n Boolean variables. We show that unless P=NP, it is not possible to approximate in polynomial time the minimum number of clauses and the minimum number of literals of pure Horn CNF representations to within a factor of 2^^1-o(1) n. This is the case even when the inputs are restricted to pure Horn 3-CNFs with O(n^1+ε) clauses, for some small positive constant ε. Furthermore, we show that even allowing sub-exponential time computation, it is still not possible to obtain constant factor approximations for such problems unless the Exponential Time Hypothesis turns out to be false.

READ FULL TEXT

Please sign up or login with your details

Forgot password? Click here to reset