Run-time efficient probabilistic model checking

Since the inception of discontinuous Galerkin (DG) methods for elliptic problems, there has existed a question of whether DG methods can be made more computationally efficient than continuous Galerkin (CG) methods. Fewer degrees of freedom, approximation properties for elliptic problems together with the number of optimization techniques, such as static condensation, available within CG framework made it challenging for DG methods to be competitive until recently. However, with the introduction of a static-condensation-amenable DG method—the hybridizable discontinuous Galerkin (HDG) method—it has become possible to perform a realistic comparison of CG and HDG methods when applied to elliptic problems. In this work, we extend upon an earlier 2D comparative study, providing numerical results and discussion of the CG and HDG method performance in three dimensions. The comparison categories covered include steady-state elliptic and time-dependent parabolic problems, various element types and serial and parallel performance. The postprocessing technique, which allows for superconvergence in the HDG case, is also discussed. Depending on the direct linear system solver used and the type of the problem (steady-state vs. time-dependent) in question the HDG method either outperforms or demonstrates a comparable performance when compared with the CG method. The HDG method however falls behind performance-wise when the iterative solver is used, which indicates the need for an effective preconditioning strategy for the method

Supporting self-adaptation via quantitative verification and sensitivity analysis at run time

Modern software-intensive systems often interact with an environment whose behavior changes over time, often unpredictably. The occurrence of changes may jeopardize their ability to meet the desired requirements. It is therefore desirable to design software in a way that it can self-adapt to the occurrence of changes with limited, or even without, human intervention. Self-adaptation can be achieved by bringing software models and model checking to run time, to support perpetual automatic reasoning about changes. Once a change is detected, the system itself can predict if requirements violations may occur and enable appropriate counter-actions. However, existing mainstream model checking techniques and tools were not conceived for run-time usage; hence they hardly meet the constraints imposed by on-the-fly analysis in terms of execution time and memory usage. This paper addresses this issue and focuses on perpetual satisfaction of non-functional requirements, such as reliability or energy consumption. Its main contribution is the description of a mathematical framework for run-time efficient probabilistic model checking. Our approach statically generates a set of verification conditions that can be efficiently evaluated at run time as soon as changes occur. The proposed approach also supports sensitivity analysis, which enables reasoning about the effects of changes and can drive effective adaptation strategies

Stochastic modeling, analysis and verification of mission-critical systems and processes

Software and business processes used in mission-critical defence applications are often characterised by stochastic behaviour. The causes for this behaviour range from unanticipated environmental changes and built-in random delays to component and communication protocol unreliability. This paper overviews the use of a stochastic modelling and analysis technique called quantitative verication to establish whether mission-critical software and business processes meet their reliability, performance and other quality-of-service requirements

Perturbation analysis in verification of discrete-time Markov chains

Perturbation analysis in probabilistic verification addresses the robustness and sensitivity problem for verification of stochastic models against qualitative and quantitative properties. We identify two types of perturbation bounds, namely non-asymptotic bounds and asymptotic bounds. Non-asymptotic bounds are exact, pointwise bounds that quantify the upper and lower bounds of the verification result subject to a given perturbation of the model, whereas asymptotic bounds are closed-form bounds that approximate non-asymptotic bounds by assuming that the given perturbation is sufficiently small. We perform perturbation analysis in the setting of Discrete-time Markov Chains. We consider three basic matrix norms to capture the perturbation distance, and focus on the computational aspect. Our main contributions include algorithms and tight complexity bounds for calculating both non-asymptotic bounds and asymptotic bounds with respect to the three perturbation distances. © 2014 Springer-Verlag