Hardness of approximate two-level logic minimization and PAC learning with membership queries

Producing a small DNF expression consistent with given data is a classical problem in computer science that occurs in a number of forms and has numerous applications. We consider two standard variants of this problem. The first one is two-level logic minimization or finding a minimum DNF formula consistent with a given complete truth table (TT-MinDNF). This problem was formulated by Quine in 1952 and has been since one of the key problems in logic design. It was proved NP-complete by Masek in 1979. The best known polynomial approximation algorithm is based on a reduction to the SET-COVER problem and produces a DNF formula of size O(d ? OPT), where d is the number of variables. We prove that TT-MinDNF is NP-hard to approximate within d for some constant > 0, establishing the first inapproximability result for the problem. The other DNF minimization problem we consider is PAC learning of DNF expressions when the learning algorithm must output a DNF expression as its hypothesis (refe...

• Type: Conference
• Year: 2006
• Where: STOC
• Authors: Vitaly Feldman
• Keywords: Algorithms, DNF Expressions, DNF Minimization Problem, Minimum Dnf Formula, STOC 2006