135 research outputs found
The Evolving University: Disruptive Change and Institutional Innovation
AbstractThe domain of education, like many institutions in contemporary society, faces significant challenges to the completion of it s mission. This is especially true of higher education, which in many countries faces increasing expectations that it serves as a driver facilitating social and cultural advancement. New modes of inclusive delivery need to be tested with real students, new curriculum approaches need to be validated, new platforms need applications and content to succeed, and analytical tools need broadly based data to be truly useful. These also include new ways of collaborating and presenting domain specific subject matter. It is increasingly likely that the University of the future will not look like present-day institutional arrangements
Smoothing a program soundly and robustly
We study the foundations of smooth interpretation, a recently-proposed program approximation scheme that facilitates the use of local numerical search techniques (e.g., gradient descent) in program analysis and synthesis. While the popular techniques for local optimization works well only on relatively smooth functions, functions encoded by real-world programs are infested with discontinuities and local irregular features. Smooth interpretation attenuates such features by taking the convolution of the program with a Gaussian function, effectively replacing discontinuous switches in the program by continuous transitions. In doing so, it extends to programs the notion of Gaussian smoothing, a popular signal-processing technique used to filter noise and discontinuities from signals.
Exact Gaussian smoothing of programs is undecidable, so algorithmic implementations of smooth interpretation must necessarily be approximate. In this paper, we characterize the approximations carried out by such algorithms. First, we identify three correctness properties—soundness, robustness, and β-robustness—that an approximate smooth interpreter should satisfy. In particular, a smooth interpreter is sound if it computes an abstraction of a program’s “smoothed” semantics, and robust if it has arbitrary-order derivatives in the input variables at every point in its input space. Second, we describe the design of an approximate smooth interpreter that provably satisfies these properties. The interpreter combines program abstraction using a new domain with symbolic calculation of convolution.National Science Foundation (U.S.) (Grant CCF-0953507)Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laborator
Traceability for Mutation Analysis in Model Transformation
International audienceModel transformation can't be directly tested using program techniques. Those have to be adapted to model characteristics. In this paper we focus on one test technique: mutation analysis. This technique aims to qualify a test data set by analyzing the execution results of intentionally faulty program versions. If the degree of qualification is not satisfactory, the test data set has to be improved. In the context of model, this step is currently relatively fastidious and manually performed. We propose an approach based on traceability mechanisms in order to ease the test model set improvement in the mutation analysis process. We illustrate with a benchmark the quick automatic identification of the input model to change. A new model is then created in order to raise the quality of the test data set
Mutation of Directed Graphs -- Corresponding Regular Expressions and Complexity of Their Generation
Directed graphs (DG), interpreted as state transition diagrams, are
traditionally used to represent finite-state automata (FSA). In the context of
formal languages, both FSA and regular expressions (RE) are equivalent in that
they accept and generate, respectively, type-3 (regular) languages. Based on
our previous work, this paper analyzes effects of graph manipulations on
corresponding RE. In this present, starting stage we assume that the DG under
consideration contains no cycles. Graph manipulation is performed by deleting
or inserting of nodes or arcs. Combined and/or multiple application of these
basic operators enable a great variety of transformations of DG (and
corresponding RE) that can be seen as mutants of the original DG (and
corresponding RE). DG are popular for modeling complex systems; however they
easily become intractable if the system under consideration is complex and/or
large. In such situations, we propose to switch to corresponding RE in order to
benefit from their compact format for modeling and algebraic operations for
analysis. The results of the study are of great potential interest to mutation
testing
The inverse moment problem for convex polytopes
The goal of this paper is to present a general and novel approach for the
reconstruction of any convex d-dimensional polytope P, from knowledge of its
moments. In particular, we show that the vertices of an N-vertex polytope in
R^d can be reconstructed from the knowledge of O(DN) axial moments (w.r.t. to
an unknown polynomial measure od degree D) in d+1 distinct generic directions.
Our approach is based on the collection of moment formulas due to Brion,
Lawrence, Khovanskii-Pukhikov, and Barvinok that arise in the discrete geometry
of polytopes, and what variously known as Prony's method, or Vandermonde
factorization of finite rank Hankel matrices.Comment: LaTeX2e, 24 pages including 1 appendi
Spotting Trees with Few Leaves
We show two results related to the Hamiltonicity and -Path algorithms in
undirected graphs by Bj\"orklund [FOCS'10], and Bj\"orklund et al., [arXiv'10].
First, we demonstrate that the technique used can be generalized to finding
some -vertex tree with leaves in an -vertex undirected graph in
time. It can be applied as a subroutine to solve the
-Internal Spanning Tree (-IST) problem in
time using polynomial space, improving upon previous algorithms for this
problem. In particular, for the first time we break the natural barrier of
. Second, we show that the iterated random bipartition employed by
the algorithm can be improved whenever the host graph admits a vertex coloring
with few colors; it can be an ordinary proper vertex coloring, a fractional
vertex coloring, or a vector coloring. In effect, we show improved bounds for
-Path and Hamiltonicity in any graph of maximum degree
or with vector chromatic number at most 8
Towards Symbolic Model-Based Mutation Testing: Combining Reachability and Refinement Checking
Model-based mutation testing uses altered test models to derive test cases
that are able to reveal whether a modelled fault has been implemented. This
requires conformance checking between the original and the mutated model. This
paper presents an approach for symbolic conformance checking of action systems,
which are well-suited to specify reactive systems. We also consider
nondeterminism in our models. Hence, we do not check for equivalence, but for
refinement. We encode the transition relation as well as the conformance
relation as a constraint satisfaction problem and use a constraint solver in
our reachability and refinement checking algorithms. Explicit conformance
checking techniques often face state space explosion. First experimental
evaluations show that our approach has potential to outperform explicit
conformance checkers.Comment: In Proceedings MBT 2012, arXiv:1202.582
Mathematical practice, crowdsourcing, and social machines
The highest level of mathematics has traditionally been seen as a solitary
endeavour, to produce a proof for review and acceptance by research peers.
Mathematics is now at a remarkable inflexion point, with new technology
radically extending the power and limits of individuals. Crowdsourcing pulls
together diverse experts to solve problems; symbolic computation tackles huge
routine calculations; and computers check proofs too long and complicated for
humans to comprehend.
Mathematical practice is an emerging interdisciplinary field which draws on
philosophy and social science to understand how mathematics is produced. Online
mathematical activity provides a novel and rich source of data for empirical
investigation of mathematical practice - for example the community question
answering system {\it mathoverflow} contains around 40,000 mathematical
conversations, and {\it polymath} collaborations provide transcripts of the
process of discovering proofs. Our preliminary investigations have demonstrated
the importance of "soft" aspects such as analogy and creativity, alongside
deduction and proof, in the production of mathematics, and have given us new
ways to think about the roles of people and machines in creating new
mathematical knowledge. We discuss further investigation of these resources and
what it might reveal.
Crowdsourced mathematical activity is an example of a "social machine", a new
paradigm, identified by Berners-Lee, for viewing a combination of people and
computers as a single problem-solving entity, and the subject of major
international research endeavours. We outline a future research agenda for
mathematics social machines, a combination of people, computers, and
mathematical archives to create and apply mathematics, with the potential to
change the way people do mathematics, and to transform the reach, pace, and
impact of mathematics research.Comment: To appear, Springer LNCS, Proceedings of Conferences on Intelligent
Computer Mathematics, CICM 2013, July 2013 Bath, U
Accelerated Model Checking of Parametric Markov Chains
Parametric Markov chains occur quite naturally in various applications: they
can be used for a conservative analysis of probabilistic systems (no matter how
the parameter is chosen, the system works to specification); they can be used
to find optimal settings for a parameter; they can be used to visualise the
influence of system parameters; and they can be used to make it easy to adjust
the analysis for the case that parameters change. Unfortunately, these
advancements come at a cost: parametric model checking is---or rather
was---often slow. To make the analysis of parametric Markov models scale, we
need three ingredients: clever algorithms, the right data structure, and good
engineering. Clever algorithms are often the main (or sole) selling point; and
we face the trouble that this paper focuses on -- the latter ingredients to
efficient model checking. Consequently, our easiest claim to fame is in the
speed-up we have often realised when comparing to the state of the art
Coverage-based quality metric of mutation operators for test suite improvement
The choice of mutation operators is a fundamental aspect in mutation testing to guide the tester to an effective test suite. Designing a set of mutation operators is subject to a trade-off between effectiveness and computational cost: a larger mutation population might uncover more faults, but will take longer to analyse. With the aim of resolving this trade-off, several authors have defined an assortment of metrics to determine the most valuable operators. In this work, we extend an existing quality metric by incorporating an additional source of data and coverage information and therefore investigate the extent to which mutants that are often covered but rarely killed can improve the evaluation of mutation operators for the refinement of the test suite. As a case study, we analyse C++ class-level operators based on the new coverage-based quality metric to assess whether the original metric is enhanced. The results when selecting the best-valued operators show that this metric has great potential to help the tester in finding effective mutation operators. In comparison with the metric from which it is derived, the use of coverage data allows to reduce the number of mutants but often loses fewer test cases and, in addition, retains those that seem hard to design
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