On implicate discovery and query optimization

Boolean expression simplification is a well-known problem in the history of Computer Science. The problem of determining prime implicates from an arbitrary Boolean expression has been mostly studied in the contexts of hardware design and automated reasoning. While many of the same principles can be applied to the simplification of search conditions in ANSI SQL queries, the richness of its language and SQL's three-valued logic present a number of challenges. We propose a modified version of a matrix-based normalization algorithm suitable for normalizing SQL search conditions in constrained-memory environments. In particular, we describe a set of tradeoffs that enable our algorithm to discover a useful set of implicates without requiring a complete conversion of the input condition to a normal form, preventing a combinatorial explosion in the number of terms.