Analysing Randomized Distributed Algorithms

In the field of model checking, abstraction refinement has proved to be an extremely successful methodology for combating the state-space explosion problem. However, little practical progress has been made in the setting of probabilistic verification. In this paper we present a novel abstraction-refinement framework for Markov decision processes (MDPs), which are widely used for modelling and verifying systems that exhibit both probabilistic and nondeterministic behaviour. Our framework comprises an abstraction approach based on stochastic two-player games, two refinement methods and an efficient algorithm for an abstraction-refinement loop. The key idea behind the abstraction approach is to maintain a separation between nondeterminism present in the original MDP and nondeterminism introduced during the abstraction process, each type being represented by a different player in the game. Crucially, this allows lower and upper bounds to be computed for the values of reachability properties of the MDP. These give a quantitative measure of the quality of the abstraction and form the basis of the corresponding refinement methods. We describe a prototype implementation of our framework and present experimental results demonstrating automatic generation of compact, yet precise, abstractions for a large selection of real-world case studies.

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“…General issues relating to abstraction in the field of probabilistic model checking are discussed in [24,34].…”

Section: Related Workmentioning

confidence: 99%

A game-based abstraction-refinement framework for Markov decision processes

Kattenbelt

Kwiatkowska

Norman

et al. 2010

Form Methods Syst Des

Self Cite

102

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“…Certain classes of probabilistic systems have been verified for arbitrary number of processes [17] e.g. Arons et al [3] present two methods for verifying liveness properties with probability 1 over parameterised probabilistic systems by converting the probabilistic system to an 'equivalent' non-deterministic one.…”

Section: Related Workmentioning

confidence: 99%

An Inductive Technique for Parameterised Model Checking of Degenerative Distributed Randomised Protocols

Graham

Calder

Miller

2009

Electronic Notes in Theoretical Computer Science

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We present a technique to tackle the parameterised probabilistic model checking problem for a particular class of randomised distributed systems, which we model as Markov Decision Processes. These systems, termed degenerative, have the property that a model of a system with some communication graph will eventually behave like a model of a system with a reduced graph. We describe an induction schema for reasoning about models of a degenerative system over arbitrary graphs. We thereby show that a certain class of quantitative LTL properties will hold for a model of a system with any communication graph if it holds for all models of a system with some base graph. We demonstrate our technique via a case study (a randomised leader election protocol) specified using the PRISM modelling language.

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“…Each action describes a transition that will update the system if the guard is true, and is selected for execution with the corresponding probability [19]. The code snippet below, taken from our model for N = 3, shows the module definition for processor P 1 .…”

Section: Prism Modelmentioning

confidence: 99%

Searching for Pareto-optimal Randomised Algorithms

Millard

White

Clark

2012

Search Based Software Engineering

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Abstract. Randomised algorithms traditionally make stochastic decisions based on the result of sampling from a uniform probability distribution, such as the toss of a fair coin. In this paper, we relax this constraint, and investigate the potential benefits of allowing randomised algorithms to use non-uniform probability distributions. We show that the choice of probability distribution influences the non-functional properties of such algorithms, providing an avenue of optimisation to satisfy non-functional requirements. We use Multi-Objective Optimisation techniques in conjunction with Genetic Algorithms to investigate the possibility of trading-off non-functional properties, by searching the space of probability distributions. Using a randomised self-stabilising token circulation algorithm as a case study, we show that it is possible to find solutions that result in Pareto-optimal trade-offs between non-functional properties, such as self-stabilisation time, service time, and fairness.

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Analysing Randomized Distributed Algorithms

Cited by 25 publications

References 88 publications

A game-based abstraction-refinement framework for Markov decision processes

A game-based abstraction-refinement framework for Markov decision processes

An Inductive Technique for Parameterised Model Checking of Degenerative Distributed Randomised Protocols

Searching for Pareto-optimal Randomised Algorithms

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