On-the-fly verification and optimization of DTA-properties for large Markov chains

Mikeev, Linar; Neuhäuβer, Martin R.; Spieler, David; Wolf, Verena

doi:10.1007/s10703-012-0165-1

Cited by 19 publications

(29 citation statements)

References 12 publications

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“…To the best of our knowledge there is no other work on stochastic models employing CSL model checking to systematic parameter exploration. The closest work is [22] where a CTMC is explored with respect to a property formalized as a deterministic timed automaton (DTA). It extends [1] to parameter estimation with respect to acceptance of the DTA.…”

Section: Introductionmentioning

confidence: 99%

Exploring Parameter Space of Stochastic Biochemical Systems Using Quantitative Model Checking

Brim

Češka

Dražan

et al. 2013

Computer Aided Verification

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We propose an automated method for exploring kinetic parameters of stochastic biochemical systems. The main question addressed is how the validity of an a priori given hypothesis expressed as a temporal logic property depends on kinetic parameters. Our aim is to compute a landscape function that, for each parameter point from the inspected parameter space, returns the quantitative model checking result for the respective continuous time Markov chain. Since the parameter space is in principle dense, it is infeasible to compute the landscape function directly. Hence, we design an effective method that iteratively approximates the lower and upper bounds of the landscape function with respect to a given accuracy. To this end, we modify the standard uniformization technique and introduce an iterative parameter space decomposition. We also demonstrate our approach on two biologically motivated case studies.

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Section: Introductionmentioning

confidence: 99%

Exploring Parameter Space of Stochastic Biochemical Systems Using Quantitative Model Checking

Brim

Češka

Dražan

et al. 2013

Computer Aided Verification

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“…The purpose of the present paper is to verify three avoidance algorithms that involve a mobile robot and a single dynamic obstacle [9]. The paths of the robot and obstacle cross each other, and their movements have the properties of Markov Decision Processes (MDPs) [21,22]. The probabilistic models and the PCTL formulae are first built, and then the PRISM software is employed to make analyses on the three avoidance strategies.…”

Section: Introductionmentioning

confidence: 99%

Modeling and Analysis of the Obstacle-Avoidance Strategies for a Mobile Robot in a Dynamic Environment

Wang

Guan

et al. 2015

Mathematical Problems in Engineering

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Obstacle avoidance is a key performance of mobile robots. However, its experimental verification is rather difficult, due to the probabilistic behaviors of both the robots and the obstacles. This paper presents the Markov Decision Process based probabilistic formal models for three obstacle-avoidance strategies of a mobile robot in an uncertain dynamic environment. The models are employed to make analyses in PRISM, and the correctness of the analysis results is verified by MATLAB simulations. Finally, the minimum time and the energy consumption are determined by further analyses in PRISM, which prove to be useful in finding the optimal strategy. The present work provides a foundation for the probabilistic formal verification of more complicated obstacleavoidance strategies.

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“…Later on, Chen et al [12] proposed approximation algorithms for time-bounded verification of several linear real-time specifications, where the restricted time-bounded case, in which the time guard x < T with a fresh clock x and a time bound T is enforced on each edge that leads to some final state of the DTA, is covered. Very recently, Mikeev et al [18] applies the notion of DTA acceptance condition on CTMCpaths to system biology. It is worth noting that Brázdil et al also studied DTA specifications in [11].…”

Section: Introductionmentioning

confidence: 99%

“…We provide tight error bounds for the approximation algorithm. Whereas other works [6,18,15] focus on single-clock DTA, our approximation scheme is applicable to any multi-clock DTA. To our knowledge, this is the first such approximation algorithm with error bounds.…”

Section: Introductionmentioning

confidence: 99%

Approximating acceptance probabilities of CTMC-paths on multi-clock deterministic timed automata

2013

Proceedings of the 16th International Conference on Hybrid Systems: Computation and Control

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We consider the problem of approximating the probability mass of the set of timed paths under a continuous-time Markov chain (CTMC) that are accepted by a deterministic timed automaton (DTA). As opposed to several existing works on this topic, we consider DTA with multiple clocks. Our key contribution is an algorithm to approximate these probabilities using finite difference methods. An error bound is provided which indicates the approximation error. The stepping stones towards this result include rigorous proofs for the measurability of the set of accepted paths and the integral-equation system characterizing the acceptance probability, and a differential characterization for the acceptance probability.

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On-the-fly verification and optimization of DTA-properties for large Markov chains

Cited by 19 publications

References 12 publications

Exploring Parameter Space of Stochastic Biochemical Systems Using Quantitative Model Checking

Exploring Parameter Space of Stochastic Biochemical Systems Using Quantitative Model Checking

Modeling and Analysis of the Obstacle-Avoidance Strategies for a Mobile Robot in a Dynamic Environment

Approximating acceptance probabilities of CTMC-paths on multi-clock deterministic timed automata

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