Order dependency in the relational model

AbstractThe relational model is formally extended to include fixed orderings on attribute domains. A new constraint, called order dependency, is then introduced to incorporate semantic information involving these orderings. It is shown that this constraint can be applied to enhance the efficiency of an implemented database. The thrust of the paper is to study logical implication for order dependency. The main theoretical results consist in (i) introducing a formalism analogous to propositional calculus for analyzing order dependency, (ii) exhibiting a sound and complete set of inference rules for order dependency, and (iii) demonstrating that determining logical implication for order dependency is co-NP-complete. It is also shown that there are sets of order dependencies for which no Armstrong relations exist

Blazes: Coordination Analysis for Distributed Programs

Distributed consistency is perhaps the most discussed topic in distributed systems today. Coordination protocols can ensure consistency, but in practice they cause undesirable performance unless used judiciously. Scalable distributed architectures avoid coordination whenever possible, but under-coordinated systems can exhibit behavioral anomalies under fault, which are often extremely difficult to debug. This raises significant challenges for distributed system architects and developers. In this paper we present Blazes, a cross-platform program analysis framework that (a) identifies program locations that require coordination to ensure consistent executions, and (b) automatically synthesizes application-specific coordination code that can significantly outperform general-purpose techniques. We present two case studies, one using annotated programs in the Twitter Storm system, and another using the Bloom declarative language.Comment: Updated to include additional materials from the original technical report: derivation rules, output stream label

An Efficient Framework for Order Optimization

Since the introduction of cost-based query optimization, the performance-critical role of interesting orders has been recognized. Some algebraic operators change interesting orders (e.g. sort and select), while others exploit interesting orders (e.g. merge join). The two operations performed by any query optimizer during plan generation are 1) computing the resulting order given an input order and an algebraic operator and 2) determining the compatibility between a given input order and the required order a given algebraic operator can beneficially exploit. Since these two operations are called millions of times during plan generation, they are highly performance-critical. The third crucial parameter is the space requirement for annotating every plan node with its output order. Lately, a powerful framework for reasoning about orders has been developed, which is based on functional dependencies. Within this framework, the current state-of-the-art algorithms for implementing the above operations both have a lower bound time requirement of Omega(n), where n is the number of functional dependencies involved. Further, the lower bound for the space requirement for every plan node is Omega(n). We improve these bounds by new algorithms with upper time bounds O(1). That is, our algorithms for both operations work in constant time during plan generation, after a one-time preparation step. Further, the upper bound for the space requirement for plan nodes is O(1) for our approach. Besides, our algorithm reduces the search space by detecting and ignoring irrelevant orderings. Experimental results with a full fledged query optimizer show that our approach significantly reduces the total time needed for plan generation. As a corollary of our experiments, it follows that the time spent for order processing is a non-neglectable part of plan generation

Rehearsal: A Configuration Verification Tool for Puppet

Large-scale data centers and cloud computing have turned system configuration into a challenging problem. Several widely-publicized outages have been blamed not on software bugs, but on configuration bugs. To cope, thousands of organizations use system configuration languages to manage their computing infrastructure. Of these, Puppet is the most widely used with thousands of paying customers and many more open-source users. The heart of Puppet is a domain-specific language that describes the state of a system. Puppet already performs some basic static checks, but they only prevent a narrow range of errors. Furthermore, testing is ineffective because many errors are only triggered under specific machine states that are difficult to predict and reproduce. With several examples, we show that a key problem with Puppet is that configurations can be non-deterministic. This paper presents Rehearsal, a verification tool for Puppet configurations. Rehearsal implements a sound, complete, and scalable determinacy analysis for Puppet. To develop it, we (1) present a formal semantics for Puppet, (2) use several analyses to shrink our models to a tractable size, and (3) frame determinism-checking as decidable formulas for an SMT solver. Rehearsal then leverages the determinacy analysis to check other important properties, such as idempotency. Finally, we apply Rehearsal to several real-world Puppet configurations.Comment: In proceedings of ACM SIGPLAN Conference on Programming Language Design and Implementation (PLDI) 201