Symbolic Model Checking of Probabilistic Processes Using MTBDDs and the Kronecker Representation

Alfaro, Luca de; Kwiatkowska, Marta; Norman, Gethin; Parker, David; Segala, Roberto

doi:10.1007/3-540-46419-0_27

Cited by 83 publications

(70 citation statements)

References 29 publications

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“…Some state-of-the-art techniques for the PMC problem in MDPs [3], [2] usually rely on symbolic methods to encode the state-action graph of the MDP in compact representations [23], [24]. Using this representation, such approaches compute the exact maximum probability of satisfying the property through an iterative method that propagates information throughout the state space.…”

Section: Probabilistic and Statistical Model Checkingmentioning

confidence: 99%

Statistical Model Checking for Markov Decision Processes

Henriques

Martins

Zuliani

et al. 2012

2012 Ninth International Conference on Quantitative Evaluation of Systems

100

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Abstract-Statistical Model Checking (SMC) is a computationally very efficient verification technique based on selective system sampling. One well identified shortcoming of SMC is that, unlike probabilistic model checking, it cannot be applied to systems featuring nondeterminism, such as Markov Decision Processes (MDP). We address this limitation by developing an algorithm that resolves nondeterminism probabilistically, and then uses multiple rounds of sampling and Reinforcement Learning to provably improve resolutions of nondeterminism with respect to satisfying a Bounded Linear Temporal Logic (BLTL) property. Our algorithm thus reduces an MDP to a fully probabilistic Markov chain on which SMC may be applied to give an approximate solution to the problem of checking the probabilistic BLTL property. We integrate our algorithm in a parallelised modification of the PRISM simulation framework. Extensive validation with both new and PRISM benchmarks demonstrates that the approach scales very well in scenarios where symbolic algorithms fail to do so.

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Section: Probabilistic and Statistical Model Checkingmentioning

confidence: 99%

Statistical Model Checking for Markov Decision Processes

Henriques

Martins

Zuliani

et al. 2012

2012 Ninth International Conference on Quantitative Evaluation of Systems

100

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“…Then, a state s satisfies the PTCL formula P ≤λ (♦φ) if and only if P(s, ♦ φ) ≤ λ. Maximal and minimal probabilities are computed by solving a linear programming problem [9,17]. The iterative algorithms implemented in Prism to solve this problem can combine different numerical computation methods with different data structures [18,27].…”

Section: Model Checking Mdpsmentioning

confidence: 99%

Automatic verification of the IEEE 1394 root contention protocol with KRONOS and PRISM

Daws

Kwiatkowska

Norman

2004

STTT

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Abstract. We report on the automatic verification of timed probabilistic properties of the IEEE 1394 root contention protocol combining two existing tools: the real-time model-checker Kronos and the probabilistic model-checker Prism. The system is modelled as a probabilistic timed automaton. We first use Kronos to perform a symbolic forward reachability analysis to generate the set of states that are reachable with non-zero probability from the initial state, and before the deadline expires. We then encode this information as a Markov decision process to be analyzed with Prism. We apply this technique to compute the minimal probability of a leader being elected before a deadline, for different deadlines, and study how this minimal probability is influenced by using a biased coin and considering different wire lengths.

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“…We now compare our symbolic implementation of time-bounded until with its sparse counterpart. For the tandem network and polling system examples, we have constructed efficient MTBDD representations of the transition matrix using the methods presented in [14] (for further details see www.cs.bham.ac.uk/~dxp/prism). This allows us to build and store much larger models with MTBDDs (given regularity) than is feasible with a sparse implementation.…”

Section: Methodsmentioning

confidence: 99%

“…So far, see e.g. [14], the sparse implementation has always outperformed the MTBDDs on quantitative numerical calculations.…”

Section: Methodsmentioning

confidence: 99%

Faster and Symbolic CTMC Model Checking

Katoen

Kwiatkowska

Norman

et al. 2001

Process Algebra and Probabilistic Methods. Performance Modelling and Verification

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Abstract. This paper reports on the implementation and the experiments with symbolic model checking of continuous-time Markov chains using multi-terminal binary decision diagrams (MTBDDs). Properties are expressed in Continuous Stochastic Logic (CSL) [7] which includes the means to express both transient and steady-state performance measures. We show that all CSL operators can be treated using standard operations on MTBDDs, thus allowing a rather straightforward implementation of symbolic CSL model checking on existing MTBDD-based platforms such as the verifier PRISM. The main result of the paper is an improvement of O(N ) in the time complexity of checking time-bounded until-formulas, where N is the number of states in the CTMC under consideration. This result yields a drastic speed-up in the verification time of model checking CTMCs, both in the symbolic and non-symbolic case.

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Symbolic Model Checking of Probabilistic Processes Using MTBDDs and the Kronecker Representation

Cited by 83 publications

References 29 publications

Statistical Model Checking for Markov Decision Processes

Statistical Model Checking for Markov Decision Processes

Automatic verification of the IEEE 1394 root contention protocol with KRONOS and PRISM

Faster and Symbolic CTMC Model Checking

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