Design by example for SQL table definitions with functional dependencies

A database is C-Armstrong for a given set of constraints in a class C if it satisfies every constraint of the set and violates every constraint in C not implied by the set. Therefore, Armstrong databases are test data that perfectly illustrate the current perceptions about the semantics of a schema. We extend the existing theory of Armstrong relations to a toolbox of Armstrong tables. That is, we investigate structural and computational properties of Armstrong tables for the class of functional dependencies (FDs) over SQL tables. Relations are special instances of SQL tables with no duplicate rows and no null value occurrences. While FDs do not enjoy Armstrong tables, the combined class of standard FDs and NOT NULL constraints does enjoy Armstrong tables. The problem of finding an Armstrong table is shown to be precisely exponential for this combined class. However, we establish an algorithm that computes Armstrong tables with a size at most quadratic in that of a minimum-sized Armstrong table. Our resulting toolbox of Armstrong tables can be applied by data engineers to concisely visualize constraints on SQL data. Such support can lead to designs that guarantee efficient data management in practice.