Model Checking CSL for Markov Population Models

Spieler, David; Hahn, Ernst Moritz; Zhang, Lijun

doi:10.4204/eptcs.154.7

Cited by 7 publications

(3 citation statements)

References 23 publications

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“…On the other hand, not discarding states allows for a simpler representation of state-to-state transitions. It also allows one to handle nested CSL formulas [Hahn et al 2009;Spieler et al 2014], for which FAU does not seem appropriate. The reason is that, when discarding a state, the information about which subformulae of the CSL formula under consideration are fulfilled is lost.…”

Section: Related Workmentioning

confidence: 98%

Computing Cumulative Rewards Using Fast Adaptive Uniformization

Dannenberg

Hahn

Kwiatkowska

2015

ACM Trans. Model. Comput. Simul.

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The computation of transient probabilities for continuous-time Markov chains often employs uniformization, also known as the Jensen method. The fast adaptive uniformization method introduced by Mateescu et al. approximates the probability by neglecting insignificant states and has proven to be effective for quantitative analysis of stochastic models arising in chemical and biological applications. However, this method has only been formulated for the analysis of properties at a given point of time t. In this article, we extend fast adaptive uniformization to handle expected reward properties that reason about the model behavior until time t, for example, the expected number of chemical reactions that have occurred until t. To show the feasibility of the approach, we integrate the method into the probabilistic model checker PRISM and apply it to a range of biological models. The performance of the method is enhanced by the use of interval splitting. We compare our implementation to standard uniformization implemented in PRISM and to fast adaptive uniformization without support for cumulative rewards implemented in MARCIE, demonstrating superior performance. ACM Reference Format:Frits Dannenberg, Ernst Moritz Hahn, and Marta Kwiatkowska. 2015. Computing cumulative rewards using fast adaptive uniformization. ACM Trans. Model.

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Section: Related Workmentioning

confidence: 98%

Computing Cumulative Rewards Using Fast Adaptive Uniformization

Dannenberg

Hahn

Kwiatkowska

2015

ACM Trans. Model. Comput. Simul.

Self Cite

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“…In the last years, scalability of analysis has become even more relevant because of the application of tool-supported, formal verification techniques to domains characterized by big data evolving in time and space, like computational biology and collective adaptive systems [102]. A widely used formalism is that of Markov population models (MPMs), for which ad-hoc algorithms for computing transient distributions [12] and to model check CSL properties [133,34] have been implemented. Enhancing scalability is the main improvement of alternative methods of performance analysis for very large systems, e.g., based on fluid approximation techniques [83,138] and on solving systems of ordinary differential equations (ODEs) [35], which is an approach allowing for producing approximated transient measures for models of 10 100 states and beyond, even thanks to (approximate) reductions [141] and aggregations [139] of ODE systems.…”

Section: Analysis Techniques and Tools: Program Analysis Model Checkmentioning

confidence: 99%

Quantitative Aspects of Programming Languages and Systems over the past 2^4 years and beyond

Aldini

2020

Electron. Proc. Theor. Comput. Sci.

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Quantitative aspects of computation are related to the use of both physical and mathematical quantities, including time, performance metrics, probability, and measures for reliability and security. They are essential in characterizing the behaviour of many critical systems and in estimating their properties. Hence, they need to be integrated both at the level of system modeling and within the verification methodologies and tools. Along the last two decades a variety of theoretical achievements and automated techniques have contributed to make quantitative modeling and verification mainstream in the research community. In the same period, they represented the central theme of the series of workshops entitled Quantitative Aspects of Programming Languages and Systems (QAPL) and born in 2001. The aim of this survey is to revisit such achievements and results from the standpoint of QAPL and its community.

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“…In this paper we consider the concept of trend in a stochastic setting, and without explicitly storing the trend in a state variable. Oscillating behaviours can be formulated either as temporal formulae [9][10][11] in CTL, PCTL or CSL or based on a system of differential equations [12]. However, for the AKAP model we have to deal with incomplete data about the reaction rates.…”

Section: Introductionmentioning

confidence: 99%

Trend-Based Analysis of a Population Model of the AKAP Scaffold Protein

Andrei

Calder

2012

Lecture Notes in Computer Science

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We formalise a continuous-time Markov chain with multidimensional discrete state space model of the AKAP scaffold protein as a crosstalk mediator between two biochemical signalling pathways. The analysis by temporal properties of the AKAP model requires reasoning about whether the counts of individuals of the same type (species) are increasing or decreasing. For this purpose we propose the concept of stochastic trends based on formulating the probabilities of transitions that increase (resp. decrease) the counts of individuals of the same type, and express these probabilities as formulae such that the state space of the model is not altered. We define a number of stochastic trend formulae (e.g. weakly increasing, strictly increasing, weakly decreasing, etc.) and use them to extend the set of state formulae of Continuous Stochastic Logic. We show how stochastic trends can be implemented in a guarded-command style specification language for transition systems. We illustrate the application of stochastic trends with numerous small examples and then we analyse the AKAP model in order to characterise and show causality and pulsating behaviours in this biochemical system.

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Model Checking CSL for Markov Population Models

Cited by 7 publications

References 23 publications

Computing Cumulative Rewards Using Fast Adaptive Uniformization

Computing Cumulative Rewards Using Fast Adaptive Uniformization

Quantitative Aspects of Programming Languages and Systems over the past 2^4 years and beyond

Trend-Based Analysis of a Population Model of the AKAP Scaffold Protein

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