Schema Polynomials and Applications

Conceptual complexity is emerging as a new bottleneck as database developers, application developers, and database administrators struggle to design and comprehend large, complex schemas. The simplicity and conciseness of a schema depends critically on the idioms available to express the schema. We propose a formal conceptual schema representation language that combines different design formalisms, and allows schema manipulation that exposes the strengths of each of these formalisms. We demonstrate how the schema factorization framework can be used to generate relational, object-oriented, and faceted physical schemas, allowing a wider exploration of physical schema alternatives than traditional methodologies. We illustrate the potential practical benefits of schema factorization by showing that simple heuristics can significantly reduce the size of a real-world schema description. We also propose the use of schema polynomials to model and derive alternative representations for complex relationships with constraints

Rewriting Declarative Query Languages

Queries against databases are formulated in declarative languages. Examples are the relational query language SQL and XPath or XQuery for querying data stored in XML. Using a declarative query language, the querist does not need to know about or decide on anything about the actual strategy a system uses to answer the query. Instead, the system can freely choose among the algorithms it employs to answer a query. Predominantly, query processing in the relational context is accomplished using a relational algebra. To this end, the query is translated into a logical algebra. The algebra consists of logical operators which facilitate the application of various optimization techniques. For example, logical algebra expressions can be rewritten in order to yield more efficient expressions. In order to query XML data, XPath and XQuery have been developed. Both are declarative query languages and, hence, can benefit from powerful optimizations. For instance, they could be evaluated using an algebraic framework. However, in general, the existing approaches are not directly utilizable for XML query processing. This thesis has two goals. The first goal is to overcome the above-mentioned misfits of XML query processing, making it ready for industrial-strength settings. Specifically, we develop an algebraic framework that is designed for the efficient evaluation of XPath and XQuery. To this end, we define an order-aware logical algebra and a translation of XPath into this algebra. Furthermore, based on the resulting algebraic expressions, we present rewrites in order to speed up the execution of such queries. The second goal is to investigate rewriting techniques in the relational context. To this end, we present rewrites based on algebraic equivalences that unnest nested SQL queries with disjunctions. Specifically, we present equivalences for unnesting algebraic expressions with bypass operators to handle disjunctive linking and correlation. Our approach can be applied to quantified table subqueries as well as scalar subqueries. For all our results, we present experiments that demonstrate the effectiveness of the developed approaches

Large substitution boxes with efficient combinational implementations

At a fundamental level, the security of symmetric key cryptosystems ties back to Claude Shannon\u27s properties of confusion and diffusion. Confusion can be defined as the complexity of the relationship between the secret key and ciphertext, and diffusion can be defined as the degree to which the influence of a single input plaintext bit is spread throughout the resulting ciphertext. In constructions of symmetric key cryptographic primitives, confusion and diffusion are commonly realized with the application of nonlinear and linear operations, respectively. The Substitution-Permutation Network design is one such popular construction adopted by the Advanced Encryption Standard, among other block ciphers, which employs substitution boxes, or S-boxes, for nonlinear behavior. As a result, much research has been devoted to improving the cryptographic strength and implementation efficiency of S-boxes so as to prohibit cryptanalysis attacks that exploit weak constructions and enable fast and area-efficient hardware implementations on a variety of platforms. To date, most published and standardized S-boxes are bijective functions on elements of 4 or 8 bits. In this work, we explore the cryptographic properties and implementations of 8 and 16 bit S-boxes. We study the strength of these S-boxes in the context of Boolean functions and investigate area-optimized combinational hardware implementations. We then present a variety of new 8 and 16 bit S-boxes that have ideal cryptographic properties and enable low-area combinational implementations

An Algebraic Approach to XQuery Optimization

As more data is stored in XML and more applications need to process this data, XML query optimization becomes performance critical. While optimization techniques for relational databases have been developed over the last thirty years, the optimization of XML queries poses new challenges. Query optimizers for XQuery, the standard query language for XML data, need to consider both document order and sequence order. Nevertheless, algebraic optimization proved powerful in query optimizers in relational and object oriented databases. Thus, this dissertation presents an algebraic approach to XQuery optimization. In this thesis, an algebra over sequences is presented that allows for a simple translation of XQuery into this algebra. The formal definitions of the operators in this algebra allow us to reason formally about algebraic optimizations. This thesis leverages the power of this formalism when unnesting nested XQuery expressions. In almost all cases unnesting nested queries in XQuery reduces query execution times from hours to seconds or milliseconds. Moreover, this dissertation presents three basic algebraic patterns of nested queries. For every basic pattern a decision tree is developed to select the most effective unnesting equivalence for a given query. Query unnesting extends the search space that can be considered during cost-based optimization of XQuery. As a result, substantially more efficient query execution plans may be detected. This thesis presents two more important cases where the number of plan alternatives leads to substantially shorter query execution times: join ordering and reordering location steps in path expressions. Our algebraic framework detects cases where document order or sequence order is destroyed. However, state-of-the-art techniques for order optimization in cost-based query optimizers have efficient mechanisms to repair order in these cases. The results obtained for query unnesting and cost-based optimization of XQuery underline the need for an algebraic approach to XQuery optimization for efficient XML query processing. Moreover, they are applicable to optimization in relational databases where order semantics are considered

Frequent Statement and Dereference Elimination for Imperative and Object-Oriented Distributed Programs

This paper introduces new approaches for the analysis of frequent statement and dereference elimination for imperative and object-oriented distributed programs running on parallel machines equipped with hierarchical memories. The paper uses languages whose address spaces are globally partitioned. Distributed programs allow defining data layout and threads writing to and reading from other thread memories. Three type systems (for imperative distributed programs) are the tools of the proposed techniques. The first type system defines for every program point a set of calculated (ready) statements and memory accesses. The second type system uses an enriched version of types of the first type system and determines which of the ready statements and memory accesses are used later in the program. The third type system uses the information gather so far to eliminate unnecessary statement computations and memory accesses (the analysis of frequent statement and dereference elimination). Extensions to these type systems are also presented to cover object-oriented distributed programs. Two advantages of our work over related work are the following. The hierarchical style of concurrent parallel computers is similar to the memory model used in this paper. In our approach, each analysis result is assigned a type derivation (serves as a correctness proof)