Periodic Reporting for period 1 - PaVeCo (Parametrised Verification and Control)
Période du rapport: 2017-11-01 au 2019-10-31
A variety of interesting systems displays stochastic behaviour. As a fully automated method to analyse such systems, stochastic model checking is an important research area. Early techniques have suffered from several shortfalls. One of these shortfalls is that the exact failure rates of components are often unavailable. In this case, parametric models can be used, where probabilities are represented by parameters rather than values.
Another shortfall is that stochastic systems are often also partially controllable. Moreover, in addition to stochastic choices, the environment of a system can be unknown or abstracted and can thus display an antagonistic behaviour. The analysis of such systems needs to account for the positive nondeterminism from the partial control over the system, the antagonistic nondeterminism that models the unknown, and the probabilistic choices. The target in this scenario is to synthesise a controller that steers the system in the best way regardless of any environment.
A third shortfall is that functional properties (safety, PCTL, LTL, or ω-regular goals) and non-functional goals (response time, energy usage) are analysed in isolation. When designing a system or inferring a control strategy, however, functional and non-functional properties are entangled and need to be considered in combination.
While parametric analysis and the analysis of stochastic systems in isolation scale to medium size systems, the analysis of systems with mixed goals is a young and rapidly developing field. We will contribute to all three aspects, but our focus will be on studying combinations between these aspects. We will develop practically efficient techniques (as opposed to techniques with good complexity), implement them, and make them available in a tool to allow for their proliferation.
Another shortfall is that stochastic systems are often also partially controllable. Moreover, in addition to stochastic choices, the environment of a system can be unknown or abstracted and can thus display an antagonistic behaviour. The analysis of such systems needs to account for the positive nondeterminism from the partial control over the system, the antagonistic nondeterminism that models the unknown, and the probabilistic choices. The target in this scenario is to synthesise a controller that steers the system in the best way regardless of any environment.
A third shortfall is that functional properties (safety, PCTL, LTL, or ω-regular goals) and non-functional goals (response time, energy usage) are analysed in isolation. When designing a system or inferring a control strategy, however, functional and non-functional properties are entangled and need to be considered in combination.
While parametric analysis and the analysis of stochastic systems in isolation scale to medium size systems, the analysis of systems with mixed goals is a young and rapidly developing field. We will contribute to all three aspects, but our focus will be on studying combinations between these aspects. We will develop practically efficient techniques (as opposed to techniques with good complexity), implement them, and make them available in a tool to allow for their proliferation.
I have worked towards improving the analysis of parametric models into two different directions:
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 contribution 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.
The analysis of parametrised systems is a growing field in verification, but the analysis of parametrised probabilistic systems is still in its infancy. This is partly because it is much harder: while there are beautiful cut-off results for non-stochastic systems that allow to focus only on small instances, there is little hope that such approaches extend to the quantitative analysis of probabilistic systems, as the probabilities depend on the size of a system. The unicorn would be an automatic trans- formation of a parametrised system into a formula, which allows to plot, say, the likelihood to reach a goal or the expected costs to do so, against the parameters of a system. While such analysis exists for narrow classes of systems, such as waiting queues, we aim both lower—stepwise exploring the parameter space—and higher—considering general systems. The novelty is to heavily exploit the similarity between instances of parametrised systems. When the parameter grows, the system for the smaller parameter is, broadly speaking, present in the larger system. We use this observation to guide the elegant state-elimination method for parametric Markov chains in such a way, that the model transformations will start with those parts of the system that are stable under increasing the parameter. We argue that this can lead to a very cheap iterative way to analyse parametric systems, show how this approach extends to reconfigurable systems, and demonstrate on two benchmarks that this approach scales.
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 contribution 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.
The analysis of parametrised systems is a growing field in verification, but the analysis of parametrised probabilistic systems is still in its infancy. This is partly because it is much harder: while there are beautiful cut-off results for non-stochastic systems that allow to focus only on small instances, there is little hope that such approaches extend to the quantitative analysis of probabilistic systems, as the probabilities depend on the size of a system. The unicorn would be an automatic trans- formation of a parametrised system into a formula, which allows to plot, say, the likelihood to reach a goal or the expected costs to do so, against the parameters of a system. While such analysis exists for narrow classes of systems, such as waiting queues, we aim both lower—stepwise exploring the parameter space—and higher—considering general systems. The novelty is to heavily exploit the similarity between instances of parametrised systems. When the parameter grows, the system for the smaller parameter is, broadly speaking, present in the larger system. We use this observation to guide the elegant state-elimination method for parametric Markov chains in such a way, that the model transformations will start with those parts of the system that are stable under increasing the parameter. We argue that this can lead to a very cheap iterative way to analyse parametric systems, show how this approach extends to reconfigurable systems, and demonstrate on two benchmarks that this approach scales.
I have increased the maximal size and complexity of parametric Markov models which can be automatically analysed. Previous parametricity of Markov models was given in terms of transition probabilities, while we have demonstrated how automatic analysis of models with a parametric structure can be achieved.