Verification of Randomized Distributed Algorithms

Segala, Roberto

doi:10.1007/3-540-44667-2_6

Cited by 157 publications

(396 citation statements)

References 60 publications

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“…Probabilistic automata (PAs) [35,36], and the closely related model of Markov decision processes (MDPs), are common formalisms for modelling systems that exhibit both probabilistic and nondeterministic behaviour. We focus here on PAs, which subsume MDPs and are particularly well suited for compositional reasoning about probabilistic systems [35].…”

Section: Modelling and Verification Of Probabilistic Systemsmentioning

confidence: 99%

“…We focus here on PAs, which subsume MDPs and are particularly well suited for compositional reasoning about probabilistic systems [35]. In each state of a PA, several possible actions can be taken and the choice between them is assumed to be resolved in a nondeterministic fashion.…”

Section: Modelling and Verification Of Probabilistic Systemsmentioning

confidence: 99%

“…A promising way to address this is to perform verification in a compositional manner, decomposing the problem into sub-tasks which analyse each component separately. However, devising compositional analysis techniques for probabilistic systems requires considerable care, particularly for models such as probabilistic automata that exhibit both probabilistic and nondeterministic behaviour [35].…”

Section: Compositional Reasoning For Probabilistic Systemsmentioning

confidence: 99%

“…In this paper, we discuss some recent developments in the area of automated compositional verification techniques for probabilistic systems, focusing on assume-guarantee verification techniques [29,21] for probabilistic automata [35,36], a natural model for compositional reasoning. When aiming to develop fully automated verification techniques, an important question that arises is how to devise suitable assumptions about system components.…”

Section: Introductionmentioning

confidence: 99%

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Automated Learning of Probabilistic Assumptions for Compositional Reasoning

Kwiatkowska

Parker

2011

Fundamental Approaches to Software Engineering

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Abstract. Probabilistic verification techniques have been applied to the formal modelling and analysis of a wide range of systems, from communication protocols such as Bluetooth, to nanoscale computing devices, to biological cellular processes. In order to tackle the inherent challenge of scalability, compositional approaches to verification are sorely needed. An example is assume-guarantee reasoning, where each component of a system is analysed independently, using assumptions about the other components that it interacts with. We discuss recent developments in the area of automated compositional verification techniques for probabilistic systems. In particular, we describe techniques to automatically generate probabilistic assumptions that can be used as the basis for compositional reasoning. We do so using algorithmic learning techniques, which have already proved to be successful for the generation of assumptions for compositional verification of non-probabilistic systems. We also present recent improvements and extensions to this work and survey some of the promising potential directions for further research in this area.

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Section: Modelling and Verification Of Probabilistic Systemsmentioning

confidence: 99%

Section: Modelling and Verification Of Probabilistic Systemsmentioning

confidence: 99%

Section: Compositional Reasoning For Probabilistic Systemsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Automated Learning of Probabilistic Assumptions for Compositional Reasoning

Kwiatkowska

Parker

2011

Fundamental Approaches to Software Engineering

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“…Probabilistic Automata [15,27,34,44,48] also provided motivation for our work, which builds upon them as deterministic hybrid systems build upon deterministic automata.…”

Section: Introductionmentioning

confidence: 99%

Stochastic Hybrid Systems: Application to Communication Networks

Hespanha

2004

Lecture Notes in Computer Science

134

122

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Abstract. We propose a model for Stochastic Hybrid Systems (SHSs) where transitions between discrete modes are triggered by stochastic events much like transitions between states of a continuous-time Markov chains. However, the rate at which transitions occur is allowed to depend both on the continuous and the discrete states of the SHS. Based on results available for Piecewise-Deterministic Markov Process (PDPs), we provide a formula for the extended generator of the SHS, which can be used to compute expectations and the overall distribution of the state. As an application, we construct a stochastic model for on-off TCP flows that considers both the congestion-avoidance and slow-start modes and takes directly into account the distribution of the number of bytes transmitted. Using the tools derived for SHSs, we model the dynamics of the moments of the sending rate by an infinite system of ODEs, which can be truncated to obtain an approximate finite-dimensional model. This model shows that, for transfer-size distributions reported in the literature, the standard deviation of the sending rate is much larger than its average. Moreover, the later seems to vary little with the probability of packet drop. This has significant implications for the design of congestion control mechanisms.

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