Computing Cumulative Rewards Using Fast Adaptive Uniformization

Dannenberg, Frits; Hahn, Ernst Moritz; Kwiatkowska, Marta

doi:10.1145/2688907

Cited by 4 publications

(4 citation statements)

References 31 publications

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“…[S ] Where S indicates that, this property calculates the average error after reaching the steady state. The same result can be obtained (in less verification time) by the following PRISM property [24]:…”

Section: The Prism Propertiessupporting

confidence: 72%

Formal Verification of Fuzzy Logic Wireless Sensor Network Localization System

Abdullah

Shehata

Ziedan

2018

The Egyptian International Journal of Engineering Sciences and

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Formal verification is mainly used to prove the correctness of safety-critical hardware and software systems. Localization problem in Wireless Sensor Network (WSN) is a hot research topic with many critical applications. Fuzzy Based Trilateration (FBT) algorithm is a simple and efficient localization technique that has been recently proposed. In this paper, we use PRISM model checker to formally verify the correctness of FBT algorithm. Our verification results show that the fuzzy rules used in the original FBT algorithm can be modified to reduce the average localization error without increasing the complexity of the algorithm. Our results also show that the localization error in the modified FBT (MFBT) algorithm is more likely to be acceptable than the original FBT algorithm.

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Section: The Prism Propertiessupporting

confidence: 72%

Formal Verification of Fuzzy Logic Wireless Sensor Network Localization System

Abdullah

Shehata

Ziedan

2018

The Egyptian International Journal of Engineering Sciences and

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“…We do not consider time-unbounded properties because of the nature of the convergence of CLA, which is guaranteed just for finite time. Since the CLA requires solving a number of differential equations that is quadratic in the number of species and independent of the population size, our methods enable formal analysis of possibly infinite-state CTMCs that cannot be analysed using classical methods based on uniformization [27,52]. Deriving model checking algorithms was challenging because the CLA yields a continuous time stochastic process with an uncountable state space.…”

Section: Discussionmentioning

confidence: 99%

“…The analysis typically involves computing the transient probability of the system residing in a state at a given time, or, for a model annotated with rewards, the expected reward that can be obtained. Despite improvements such as symmetry reduction [33], sliding window [52] and fast adaptive uniformisation [26], their practical use for Stochastic Reaction Networks is severely hindered by state space explosion [33], which in a SRN grows exponentially with the number of molecules when finite, and may be infinite, in which case finite projection methods have to be used [43]. As a consequence, approximate but faster algorithms are appealing.…”

Section: Introductionmentioning

confidence: 99%

Central Limit Model Checking

Bortolussi

Cardelli

Kwiatkowska

et al. 2019

ACM Trans. Comput. Logic

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We consider probabilistic model checking for continuoustime Markov chains (CTMCs) induced from Stochastic Reaction Networks (SRNs) against a fragment of Continuous Stochastic Logic (CSL) extended with reward operators. Classical numerical algorithms for CSL model checking based on uniformisation are limited to finite CTMCs and suffer from exponential growth of the state space with respect to the number of species. On the other hand, approximate techniques such as mean-field approximations and simulations combined with statistical inference are more scalable, but can be time consuming and do not support the full expressiveness of CSL. In this paper we employ a continuousspace approximation of the CTMC in terms of a Gaussian process based on the Central Limit Approximation (CLA), also known as the Linear Noise Approximation (LNA), whose solution requires solving a number of differential equations that is quadratic in the number of species and independent of the population size. We then develop efficient and scalable approximate model checking algorithms on the resulting Gaussian process, where we restrict the target regions for probabilistic reachability to convex polytopes. This allows us to derive an abstraction in terms of a time-inhomogeneous discrete-time Markov chain (DTMC), whose dimension is independent of the number of species, on which model checking is performed. Using results from probability theory, we prove the convergence in distribution of our algorithms to the corresponding measures on the original CTMC. We implement the techniques and, on a set of examples, demonstrate that they allow us to overcome the state space explosion problem, while still correctly characterizing the stochastic behaviour of the system. Our methods can be used for formal analysis of a wide range of distributed stochastic systems, including biochemical systems, sensor networks and population protocols.

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“…The CME can be equivalently defined in terms of the infinitesimal generator matrix [37], which admits computing an approximation of the CME using, for example, fast adaptive uniformisation [14,13] or the sliding window method [37]. We also define the CTMC ( X N (t)…”

Section: Introductionmentioning

confidence: 99%

Stochastic Analysis of Chemical Reaction Networks Using Linear Noise Approximation

Cardelli

Kwiatkowska

Laurenti

2015

Computational Methods in Systems Biology

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Stochastic evolution of Chemical Reactions Networks (CRNs) over time is usually analysed through solving the Chemical Master Equation (CME) or performing extensive simulations. Analysing stochasticity is often needed, particularly when some molecules occur in low numbers. Unfortunately, both approaches become infeasible if the system is complex and/or it cannot be ensured that initial populations are small. We develop a probabilistic logic for CRNs that enables stochastic analysis of the evolution of populations of molecular species. We present an approximate model checking algorithm based on the Linear Noise Approximation (LNA) of the CME, whose computational complexity is independent of the population size of each species and polynomial in the number of different species. The algorithm requires the solution of first order polynomial differential equations. We prove that our approach is valid for any CRN close enough to the thermodynamical limit. However, we show on four case studies that it can still provide good approximation even for low molecule counts. Our approach enables rigorous analysis of CRNs that are not analyzable by solving the CME, but are far from the deterministic limit. Moreover, it can be used for a fast approximate stochastic characterization of a CRN.

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Computing Cumulative Rewards Using Fast Adaptive Uniformization

Cited by 4 publications

References 31 publications

Formal Verification of Fuzzy Logic Wireless Sensor Network Localization System

Formal Verification of Fuzzy Logic Wireless Sensor Network Localization System

Central Limit Model Checking

Stochastic Analysis of Chemical Reaction Networks Using Linear Noise Approximation

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