Database Queries that Explain their Work

Provenance for database queries or scientific workflows is often motivated as providing explanation, increasing understanding of the underlying data sources and processes used to compute the query, and reproducibility, the capability to recompute the results on different inputs, possibly specialized to a part of the output. Many provenance systems claim to provide such capabilities; however, most lack formal definitions or guarantees of these properties, while others provide formal guarantees only for relatively limited classes of changes. Building on recent work on provenance traces and slicing for functional programming languages, we introduce a detailed tracing model of provenance for multiset-valued Nested Relational Calculus, define trace slicing algorithms that extract subtraces needed to explain or recompute specific parts of the output, and define query slicing and differencing techniques that support explanation. We state and prove correctness properties for these techniques and present a proof-of-concept implementation in Haskell.Comment: PPDP 201

On the computational complexity of dynamic slicing problems for program schemas

This is the preprint version of the Article - Copyright @ 2011 Cambridge University PressGiven a program, a quotient can be obtained from it by deleting zero or more statements. The field of program slicing is concerned with computing a quotient of a program that preserves part of the behaviour of the original program. All program slicing algorithms take account of the structural properties of a program, such as control dependence and data dependence, rather than the semantics of its functions and predicates, and thus work, in effect, with program schemas. The dynamic slicing criterion of Korel and Laski requires only that program behaviour is preserved in cases where the original program follows a particular path, and that the slice/quotient follows this path. In this paper we formalise Korel and Laski's definition of a dynamic slice as applied to linear schemas, and also formulate a less restrictive definition in which the path through the original program need not be preserved by the slice. The less restrictive definition has the benefit of leading to smaller slices. For both definitions, we compute complexity bounds for the problems of establishing whether a given slice of a linear schema is a dynamic slice and whether a linear schema has a non-trivial dynamic slice, and prove that the latter problem is NP-hard in both cases. We also give an example to prove that minimal dynamic slices (whether or not they preserve the original path) need not be unique.This work was partly supported by the Engineering and Physical Sciences Research Council, UK, under grant EP/E002919/1

Control dependence for extended finite state machines

Though there has been nearly three decades of work on program slicing, there has been comparatively little work on slicing for state machines. One of the primary challenges that currently presents a barrier to wider application of state machine slicing is the problem of determining control dependence. We survey existing related definitions, introducing a new definition that subsumes one and extends another. We illustrate that by using this new definition our slices respect Weiser slicing’s termination behaviour. We prove results that clarify the relationships between our definition and older ones, following this up with examples to motivate the need for these differences

Amorphous slicing of extended finite state machines

Slicing is useful for many Software Engineering applications and has been widely studied for three decades, but there has been comparatively little work on slicing Extended Finite State Machines (EFSMs). This paper introduces a set of dependency based EFSM slicing algorithms and an accompanying tool. We demonstrate that our algorithms are suitable for dependence based slicing. We use our tool to conduct experiments on ten EFSMs, including benchmarks and industrial EFSMs. Ours is the first empirical study of dependence based program slicing for EFSMs. Compared to the only previously published dependence based algorithm, our average slice is smaller 40% of the time and larger only 10% of the time, with an average slice size of 35% for termination insensitive slicing

Towards an Efficient Use of the BLAS Library for Multilinear Tensor Contractions

Mathematical operators whose transformation rules constitute the building blocks of a multi-linear algebra are widely used in physics and engineering applications where they are very often represented as tensors. In the last century, thanks to the advances in tensor calculus, it was possible to uncover new research fields and make remarkable progress in the existing ones, from electromagnetism to the dynamics of fluids and from the mechanics of rigid bodies to quantum mechanics of many atoms. By now, the formal mathematical and geometrical properties of tensors are well defined and understood; conversely, in the context of scientific and high-performance computing, many tensor- related problems are still open. In this paper, we address the problem of efficiently computing contractions among two tensors of arbitrary dimension by using kernels from the highly optimized BLAS library. In particular, we establish precise conditions to determine if and when GEMM, the kernel for matrix products, can be used. Such conditions take into consideration both the nature of the operation and the storage scheme of the tensors, and induce a classification of the contractions into three groups. For each group, we provide a recipe to guide the users towards the most effective use of BLAS.Comment: 27 Pages, 7 figures and additional tikz generated diagrams. Submitted to Applied Mathematics and Computatio