Implementation of a Database System with Boolean Algebra Constraints

This thesis describes an implementation of a constraint database system with constraints over a Boolean Algebra of sets. The system allows within the input database as well as the queries equality, subset-equality and monotone inequality constraints between Boolean Algebra terms built up using the operators of union, intersection and complement. Hence the new system extends the earlier DISCO system, which only allowed equality and subset-equality constraints between Boolean algebra variables and constants. The new system allows Datalog with Boolean Algebra constraints as the query lan- guage. The implementation includes an extension of Naive and Semi-Naive evaluation methods for Datalog programs and algebraic optimization techniques for relational algebra formulas. The thesis also includes three example applications of the new system in the area of family tree genealogy, genome map assembly, and two-player game analysis. In each of these three cases the optimization provides a significant improvement in the running time of the queries. Advisor: Peter Z. Reves

The Evaluation and the Computational Complexity of Datalog Queries of Boolean Constraint Databases

In the database framework of Kanellakis et al. it was argued that constraint query languages should meet the closed-form requirement, that is, they should take as input constraint databases and give as output constraint databases that use the same type of constraints. This paper shows that the closed-form requirement can be met for Datalog queries with Boolean equality constraints with double exponential time-complete data complexity, for Datalog queries with precedence and monotone inequality constraints in triple exponential-time data complexity. A closed-form evaluation is also shown for (Stratified) Datalog queries with equality and inequality constraints in atomless Boolean algebras in triple exponential-time data complexity. 1 Introduction Constraint databases describe extensional database relations as quantifier-free first-order formulas. Constraint databases in the form of non-ground facts have been used in constraint logic programming [9, 10, 19] for almost ten years. Constra..