A Generalized-Zero-Preserving Method for Compact Encoding of Concept Lattices

Constructing an encoding of a concept lattice using short bit vectors allows for efficient computation of join operations on the lattice. Join is the central operation any unification-based parser must support. We extend the traditional bit vector encoding, which represents join failure using the zero vector, to count any vector with less than a fixed number of one bits as failure. This allows non-joinable elements to share bits, resulting in a smaller vector size. A constraint solver is used to construct the encoding, and a variety of techniques are employed to find near-optimal solutions and handle timeouts. An evaluation is provided comparing the extended representation of failure with traditional bit vector