Solving Functional Constraints by Variable Substitution

Functional constraints and bi-functional constraints are an important constraint class in Constraint Programming (CP) systems, in particular for Constraint Logic Programming (CLP) systems. CP systems with finite domain constraints usually employ CSP-based solvers which use local consistency, for example, arc consistency. We introduce a new approach which is based instead on variable substitution. We obtain efficient algorithms for reducing systems involving functional and bi-functional constraints together with other non-functional constraints. It also solves globally any CSP where there exists a variable such that any other variable is reachable from it through a sequence of functional constraints. Our experiments on random problems show that variable elimination can significantly improve the efficiency of solving problems with functional constraints

Stochastic Database Cracking: Towards Robust Adaptive Indexing in Main-Memory Column-Stores

Modern business applications and scientific databases call for inherently dynamic data storage environments. Such environments are characterized by two challenging features: (a) they have little idle system time to devote on physical design; and (b) there is little, if any, a priori workload knowledge, while the query and data workload keeps changing dynamically. In such environments, traditional approaches to index building and maintenance cannot apply. Database cracking has been proposed as a solution that allows on-the-fly physical data reorganization, as a collateral effect of query processing. Cracking aims to continuously and automatically adapt indexes to the workload at hand, without human intervention. Indexes are built incrementally, adaptively, and on demand. Nevertheless, as we show, existing adaptive indexing methods fail to deliver workload-robustness; they perform much better with random workloads than with others. This frailty derives from the inelasticity with which these approaches interpret each query as a hint on how data should be stored. Current cracking schemes blindly reorganize the data within each query's range, even if that results into successive expensive operations with minimal indexing benefit. In this paper, we introduce stochastic cracking, a significantly more resilient approach to adaptive indexing. Stochastic cracking also uses each query as a hint on how to reorganize data, but not blindly so; it gains resilience and avoids performance bottlenecks by deliberately applying certain arbitrary choices in its decision-making. Thereby, we bring adaptive indexing forward to a mature formulation that confers the workload-robustness previous approaches lacked. Our extensive experimental study verifies that stochastic cracking maintains the desired properties of original database cracking while at the same time it performs well with diverse realistic workloads.Comment: VLDB201

Benchmarking Symbolic Execution Using Constraint Problems -- Initial Results

Symbolic execution is a powerful technique for bug finding and program testing. It is successful in finding bugs in real-world code. The core reasoning techniques use constraint solving, path exploration, and search, which are also the same techniques used in solving combinatorial problems, e.g., finite-domain constraint satisfaction problems (CSPs). We propose CSP instances as more challenging benchmarks to evaluate the effectiveness of the core techniques in symbolic execution. We transform CSP benchmarks into C programs suitable for testing the reasoning capabilities of symbolic execution tools. From a single CSP P, we transform P depending on transformation choice into different C programs. Preliminary testing with the KLEE, Tracer-X, and LLBMC tools show substantial runtime differences from transformation and solver choice. Our C benchmarks are effective in showing the limitations of existing symbolic execution tools. The motivation for this work is we believe that benchmarks of this form can spur the development and engineering of improved core reasoning in symbolic execution engines

A Comparison of SAT Encodings for Acyclicity of Directed Graphs

Many practical applications require synthesizing directed graphs that satisfy the acyclic constraint along with some side constraints. Several methods have been devised for encoding acyclicity of directed graphs into SAT, each of which is based on a cycle-detecting algorithm. The leaf-elimination encoding (LEE) repeatedly eliminates leaves from the graph, and judges the graph to be acyclic if the graph becomes empty at a certain time. The vertex-elimination encoding (VEE) exploits the property that the cyclicity of the resulting graph produced by the vertex-elimination operation entails the cyclicity of the original graph. While VEE is significantly smaller than the transitive-closure encoding for sparse graphs, it generates prohibitively large encodings for large dense graphs. This paper reports on a comparison study of four SAT encodings for acyclicity of directed graphs, namely, LEE using unary encoding for time variables (LEE-u), LEE using binary encoding for time variables (LEE-b), VEE, and a hybrid encoding which combines LEE-b and VEE. The results show that the hybrid encoding significantly outperforms the others

Set Intersection and Consistency in Constraint Networks

Abstract In this paper, we show that there is a close relation between consistency in a constraint network and set intersection. A proof schema is provided as a generic way to obtain consistency properties from properties on set intersection. This approach not only simplifies the understanding of and unifies many existing consistency results, but also directs the study of consistency to that of set intersection properties in many situations, as demonstrated by the results on the convexity and tightness of constraints in this paper. Specifically, we identify a new class of tree convex constraints where local consistency ensures global consistency. This generalizes row convex constraints. Various consistency results are also obtained on constraint networks where only some, in contrast to all in the existing work, constraints are tight

Robust Controllability in Temporal Constraint Networks under Uncertainty

10.1109/ICTAI.2006.100Proceedings - International Conference on Tools with Artificial Intelligence, ICTAI288-296PCTI