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

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

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 $k$-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 $k$-vertex tree with $l$ leaves in an $n$-vertex undirected graph in $O^*(1.657^k2^{l/2})$ time. It can be applied as a subroutine to solve the $k$-Internal Spanning Tree ($k$-IST) problem in $O^*(\min(3.455^k, 1.946^n))$ time using polynomial space, improving upon previous algorithms for this problem. In particular, for the first time we break the natural barrier of $O^*(2^n)$. 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 $k$-Path and Hamiltonicity in any graph of maximum degree $\Delta=4,\ldots,12$ 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

Mutation Operators for UML Class Diagrams

La prueba de mutación es una técnica bien establecida para evaluar la calidad de los casos de prueba al verificar qué tan bien detectan fallas inyectadas en un artefacto de software (mutante). Usando esta técnica, la actividad más crítica es el diseño adecuado de operadores de mutación para que reflejen defectos típicos del artefacto bajo prueba. Este artículo presenta el diseño de un conjunto de operadores de mutación para esquemas conceptuales (CS) basados en diagramas de clase UML (CD). En este documento, los operadores se definen de acuerdo con una clasificación de defectos existente para UML CS y elementos relevantes identificados a partir del metamodelo UML-CD. Los operadores se utilizan posteriormente para generar mutantes de primer orden para un CS bajo prueba. Finalmente, para analizar la utilidad de los operadores de mutación, medimos algunas características básicas de los operadores de mutación con tres CS diferentes bajo prueba.Mutation Testing is a well-established technique for assessing the quality of test cases by checking how well they detect faults injected into a software artefact (mutant). Using this technique, the most critical activity is the adequate design of mutation operators so that they reflect typical defects of the artefact under test. This paper presents the design of a set of mutation operators for Conceptual Schemas (CS) based on UML Class Diagrams (CD). In this paper, the operators are defined in accordance with an existing defects classification for UML CS and relevant elements identified from the UML-CD meta-model. The operators are subsequently used to generate first order mutants for a CS under test. Finally, in order to analyse the usefulness of the mutation operators, we measure some basic characteristics of mutation operators with three different CSs under test.Ljubljan

Practical Verification of Decision-Making in Agent-Based Autonomous Systems

We present a verification methodology for analysing the decision-making component in agent-based hybrid systems. Traditionally hybrid automata have been used to both implement and verify such systems, but hybrid automata based modelling, programming and verification techniques scale poorly as the complexity of discrete decision-making increases making them unattractive in situations where complex log- ical reasoning is required. In the programming of complex systems it has, therefore, become common to separate out logical decision-making into a separate, discrete, component. However, verification techniques have failed to keep pace with this devel- opment. We are exploring agent-based logical components and have developed a model checking technique for such components which can then be composed with a sepa- rate analysis of the continuous part of the hybrid system. Among other things this allows program model checkers to be used to verify the actual implementation of the decision-making in hybrid autonomous systems