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Title:
Multiphase until formulas over Markov reward models: An algebraic approach
Author: Xu, M ; Zhang, LJ ; Jansen, DN ; Zhu, HB ; Yang, ZY
Keyword: Probabilistic model checking ; Markov reward model ; Continuous stochastic logic ; Cylindrical algebraic decomposition ; Transcendental number
Source: THEORETICAL COMPUTER SCIENCE
Issued Date: 2016
Volume: 611, Pages:116-135
Indexed Type: SCI
Department: E China Normal Univ, Shanghai Key Lab Multidimens Informat Proc, Shanghai 200062, Peoples R China. E China Normal Univ, Dept Comp Sci & Technol, Shanghai 200062, Peoples R China. Chinese Acad Sci, Inst Software, State Key Lab Comp Sci, Beijing, Peoples R China. Radboud Univ Nijmegen, Model Based Syst Dev, NL-6525 ED Nijmegen, Netherlands. E China Normal Univ, Shanghai Key Lab Trustworthy Comp, Shanghai 200062, Peoples R China.
Abstract: We consider the probabilistic model checking problem of continuous-time Markov chains with rewards. We first extend multiphase until formulas in continuous stochastic logic (CSL) with reward constraints. Then we present an effective integral-style algorithm to compute the probability under the assumption of harmony, and give upper and lower bounds of the probability without this assumption. Furthermore, the resulting probability value (or its upper and lower bounds) is shown to be a real number of a well-formed structure, with which we can successfully (or partially) decide whether the constraints in the CSL formula are satisfied. Our method is entirely based on algebraic manipulations and number theory. Finally, to show the practical usefulness, we apply the results to evaluate the performance of a small multi-processor system. (C) 2015 Elsevier B.V. All rights reserved.
English Abstract: We consider the probabilistic model checking problem of continuous-time Markov chains with rewards. We first extend multiphase until formulas in continuous stochastic logic (CSL) with reward constraints. Then we present an effective integral-style algorithm to compute the probability under the assumption of harmony, and give upper and lower bounds of the probability without this assumption. Furthermore, the resulting probability value (or its upper and lower bounds) is shown to be a real number of a well-formed structure, with which we can successfully (or partially) decide whether the constraints in the CSL formula are satisfied. Our method is entirely based on algebraic manipulations and number theory. Finally, to show the practical usefulness, we apply the results to evaluate the performance of a small multi-processor system. (C) 2015 Elsevier B.V. All rights reserved.
Language: 英语
WOS ID: WOS:000369211000004
Citation statistics:
Content Type: 期刊论文
URI: http://ir.iscas.ac.cn/handle/311060/17413
Appears in Collections:软件所图书馆_期刊论文

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Recommended Citation:
Xu, M,Zhang, LJ,Jansen, DN,et al. Multiphase until formulas over Markov reward models: An algebraic approach[J]. THEORETICAL COMPUTER SCIENCE,2016-01-01,611:116-135.
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