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| Multiphase until formulas over Markov reward models: An algebraic approach | |
| Xu, M; Zhang, LJ; Jansen, DN; Zhu, HB; Yang, ZY | |
| 2016 | |
| Source | THEORETICAL COMPUTER SCIENCE
 |
| ISSN | 0304-3975 |
| Volume | 611Pages:116-135 |
| 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.; 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. |
| Indexed Type | SCI |
| Keyword | Probabilistic Model Checking Markov Reward Model Continuous Stochastic Logic Cylindrical Algebraic Decomposition Transcendental Number |
| 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. |
| Language | 英语 |
| WOS ID | WOS:000369211000004 |
| Citation statistics | |
| Content Type | 期刊论文 |
| URI | http://ir.iscas.ac.cn/handle/311060/17413 |
| Collection | 中国科学院软件研究所 |
| Recommended Citation GB/T 7714 | Xu, M,Zhang, LJ,Jansen, DN,et al. Multiphase until formulas over Markov reward models: An algebraic approach[J]. THEORETICAL COMPUTER SCIENCE,2016,611:116-135. |
| APA | Xu, M,Zhang, LJ,Jansen, DN,Zhu, HB,&Yang, ZY.(2016).Multiphase until formulas over Markov reward models: An algebraic approach.THEORETICAL COMPUTER SCIENCE,611,116-135. |
| MLA | Xu, M,et al."Multiphase until formulas over Markov reward models: An algebraic approach".THEORETICAL COMPUTER SCIENCE 611(2016):116-135. |
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| 1-s2.0-S030439751500（614KB） | 开放获取 | License | Application Full Text | |||
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