Algebra Seminar talk
Minimum Hamming Distance of Boolean Propositional Models
We study the minimum Hamming distance between distinct satisfying assignments of a conjunctive input formula over a given set of Boolean relations (MinSolutionDistance, MSD). We present a complete classification of the complexity of this optimization problem with respect to the relations admitted in the formula. We give polynomial time algorithms for several classes of constraint languages. For all other cases we prove hardness or completeness with respect to poly-APX, or NPO, or equivalence to a well-known hard optimization problem.
This is joint work with Miki Hermann, Stefan Mengel, and Gernot Salzer. Supported by FWF grant I836-N23, ANR-11-ISO2-003-01 Blanc International grant ALCOCLAN, and QUALCOMM grant