Consistency and Certain Answers in Relational to RDF Data Exchange with Shape Constraints

We investigate the data exchange from relational databases to RDF graphs inspired by R2RML with the addition of target shape schemas. We study the problems of consistency i.e., checking that every source instance admits a solution, and certain query answering i.e., finding answers present in every solution. We identify the class of constructive relational to RDF data exchange that uses IRI constructors and full tgds (with no existential variables) in its source to target dependencies. We show that the consistency problem is coNP-complete. We introduce the notion of universal simulation solution that allows to compute certain query answers to any class of queries that is robust under simulation. One such class are nested regular expressions (NREs) that are forward i.e., do not use the inverse operation. Using universal simulation solution renders tractable the computation of certain answers to forward NREs (data-complexity). Finally, we present a number of results that show that relaxing the restrictions of the proposed framework leads to an increase in complexity

Deciding Second-order Logics using Database Evaluation Techniques

We outline a novel technique that maps the satisfiability problems of second-order logics, in particular WSnS (weak monadic second-order logic with n successors), S1S (monadic second-order logic with one successor), and of μ-calculus, to the problem of query evaluation of Complex-value Datalog queries. In this dissertation, we propose techniques that use database evaluation and optimization techniques for automata-based decision procedures for the above logics. We show how the use of advanced implementation techniques for Deductive databases and for Logic Programs, in particular the use of tabling, yields a considerable improvement in performance over more traditional approaches. We also explore various optimizations of the proposed technique, in particular we consider variants of tabling and goal reordering. We then show that the decision problem for S1S can be mapped to the problem of query evaluation of Complex-value Datalog queries. We explore optimizations that can be applied to various types of formulas. Last, we propose analogous techniques that allow us to approach μ-calculus satisfiability problem in an incremental fashion and without the need for re-computation. In addition, we outline a top-down evaluation technique to drive our incremental procedure and propose heuristics that guide the problem partitioning to reduce the size of the problems that need to be solved

Language Containment of Non-Deterministic Omega-Automata

. Algorithms and techniques to determinize and complement !-automata with various forms of fairness constraints are investigated and implemented. A tool-box is constructed by supplementing these algorithms with less complex ones for certain special cases. Recently published constructions which are asymptotically optimum constitute some of the core routines. The principal use of these tools is in checking language containment between two non-deterministic automata. In language containment based verification, the need for this check may arise in two occasions: when checking whether a system satisfies a property expressed as a non-deterministic automaton, or, in hierarchical verification, where the more detailed system description must satisfy the more abstract specification. We give examples motivating the utility of non-deterministic specifications and complexity results relating non-deterministic and deterministic !-automata. The algorithms mentioned have been implemented as part of..