## On statistical model checking of stochastic systems (2005)

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Venue: | In Etessami, K., Rajamani, S.K., eds.: CAV. Volume 3576 of Lecture Notes in Computer Science |

Citations: | 28 - 2 self |

### BibTeX

@INPROCEEDINGS{Sen05onstatistical,

author = {Koushik Sen and Mahesh Viswanathan and Gul Agha},

title = {On statistical model checking of stochastic systems},

booktitle = {In Etessami, K., Rajamani, S.K., eds.: CAV. Volume 3576 of Lecture Notes in Computer Science},

year = {2005},

pages = {266--280},

publisher = {Springer}

}

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### Abstract

Abstract. Statistical methods to model check stochastic systems have been, thus far, developed only for a sublogic of continuous stochastic logic (CSL) that does not have steady state operator and unbounded until formulas. In this paper, we present a statistical model checking algorithm that also verifies CSL formulas with unbounded untils. The algorithm is based on Monte Carlo simulation of the model and hypothesis testing of the samples, as opposed to sequential hypothesis testing. We have implemented the algorithm in a tool called VESTA, and found it to be effective in verifying several examples. 1

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Introduction to the Numerical Solution of Markov Chains
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Citation Context ... formula in our concerned logic (CSL or PCTL), is measurable. 3. The number of states of the system is finite. It has been shown that commonly used models such as continuous-time Markov chains (CTMC) =-=[17]-=-, semi-Markov chains (SMC) [7, 14], which are a generalization of CTMC, meet the above requirements. While we believe our algorithm will work for any model that satisfies the above conditions, in orde... |

245 | A logic for reasoning about time and reliability
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Citation Context ...it to be effective in verifying several examples. 1 Introduction Stochastic models and temporal logics such as continuous stochastic logic (CSL) [1, 3] and probabilistic computation tree logic (PCTL) =-=[9]-=- are widely used to model practical systems and analyze their performance and reliability. There are two primary approaches to analyzing the stochastic behavior of such systems: numerical and statisti... |

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Citation Context ... (CSL or PCTL), is measurable. 3. The number of states of the system is finite. It has been shown that commonly used models such as continuous-time Markov chains (CTMC) [17], semi-Markov chains (SMC) =-=[7, 14]-=-, which are a generalization of CTMC, meet the above requirements. While we believe our algorithm will work for any model that satisfies the above conditions, in order to establish the mathematical co... |

185 | Prism: Probabilistic symbolic model checker
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Citation Context ...ecked for correctness with respect to the specification using symbolic and numerical methods. Model checkers for different classes of stochastic processes and specification logics have been developed =-=[10, 13, 12, 4, 5, 14, 2]-=-. Although the numerical approach is highly accurate, it suffers from memory problem due to state-space explosion and being computationally intensive. An alternate method, proposed in [18], is based o... |

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Citation Context ...ψ over a path π will be denoted by A(π,ψ,α,β). Note that A(M,φ,α ∗ ,β ∗ ) is same as A(sI,φ,α ∗ ,β ∗ ). 3.1 Probabilistic Operator: Computing A(s, P⊲⊳p(ψ), α, β) We use statistical hypothesis testing =-=[11]-=- to verify a probabilistic property φ = P⊲⊳p(ψ) at a given state s. Without loss of generality, we show our procedure for φ = P≥p(ψ). Note that P<p(ψ) is the same as ¬P≥p(ψ) and < (or >) is essentiall... |

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Citation Context ...ecked for correctness with respect to the specification using symbolic and numerical methods. Model checkers for different classes of stochastic processes and specification logics have been developed =-=[10, 13, 12, 4, 5, 14, 2]-=-. Although the numerical approach is highly accurate, it suffers from memory problem due to state-space explosion and being computationally intensive. An alternate method, proposed in [18], is based o... |

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75 | Probabilistic verification of discrete event systems using acceptance sampling
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Citation Context ...12, 4, 5, 14, 2]. Although the numerical approach is highly accurate, it suffers from memory problem due to state-space explosion and being computationally intensive. An alternate method, proposed in =-=[18]-=-, is based on Monte Carlo simulation of the model and performing sequential hypothesis testing on the sample generated. In [15], this method was extended to statistically verify black-box, deployed sy... |

59 |
Model-checking continuous-time markov chains
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Citation Context ...mented the algorithm in a tool called VESTA, and found it to be effective in verifying several examples. 1 Introduction Stochastic models and temporal logics such as continuous stochastic logic (CSL) =-=[1, 3]-=- and probabilistic computation tree logic (PCTL) [9] are widely used to model practical systems and analyze their performance and reliability. There are two primary approaches to analyzing the stochas... |

55 | Multi terminal binary decision diagrams to represent and analyse continuous time Markov chains
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Citation Context ...blem. The plot shows the performance of the tool with caching turned on (with no discount optimization). Tandem Queuing Network: This case study is based on a simple tandem queuing network studied in =-=[11]-=-. The model is represented as a CTMC which consists of a M/Cox2/1-queue sequentially composed with a M/M/1-queue. We 11stime in sec 10 3 10 2 10 1 10 0 T=5 T=50 T=500 10 -1 10 0 10 1 10 2 10 3 10 4 10... |

49 | Stochastic Petri Net Models of Polling Systems - Ibe, Trivedi - 1990 |

48 | Numerical vs. statistical probabilistic model checking
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- 2006
(Show Context)
Citation Context ...d until formulas over a DTMC model. We also report the performance of our tool in verifying two CTMC models (one of them is provided in the appendix due to space constraints) used for case studies in =-=[20]-=-. The experiments were done on a single-processor 2GHz Pentium M laptop with 1GB SDRAM running Windows XP. IPv4 ZeroConf Protocol: We picked the DTMC model of the IPv4 ZeroConf Protocol described in [... |

45 |
Verifying continuous-time Markov Chains
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Citation Context ...mented the algorithm in a tool called VESTA, and found it to be effective in verifying several examples. 1 Introduction Stochastic models and temporal logics such as continuous stochastic logic (CSL) =-=[1, 3]-=- and probabilistic computation tree logic (PCTL) [9] are widely used to model practical systems and analyze their performance and reliability. There are two primary approaches to analyzing the stochas... |

45 | A Markov chain model checker
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- 2000
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Citation Context |

42 | Statistical Model Checking of Black-Box Probabilistic Systems
- Sen, Viswanathan, et al.
- 2004
(Show Context)
Citation Context ...on and being computationally intensive. An alternate method, proposed in [18], is based on Monte Carlo simulation of the model and performing sequential hypothesis testing on the sample generated. In =-=[15]-=-, this method was extended to statistically verify black-box, deployed systems that can only be passively observed. Being statistical, these methods are less precise: they only provide probabilistic g... |

33 | Verifying quantitative properties of continuous probabilistic timed automata
- Kwiatkowska, Norman, et al.
- 2000
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24 | Beyond memoryless distributions: Model checking semi-Markov chains
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7 |
On statistical model checking of probabilistic systems
- Sen, Viswanathan, et al.
- 2005
(Show Context)
Citation Context ...one may easily pick ps to be c/N where N is the number of states and c is some positive constant. This will ensure that δ2 the upper bound of the range in condition C2 is (1−c/N) N ≤ δ22ec (proved in =-=[16]-=-), which can be made as close to 0 as desired by a suitable choice of c. Note that making ps smaller comes with a price: if we make ps very small, the expected length of the samples increases. This ca... |

6 | Cost-optimization of the IPv4 zeroconf protocol
- Bohnenkamp, Stok, et al.
- 2003
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Citation Context ...]. The experiments were done on a single-processor 2GHz Pentium M laptop with 1GB SDRAM running Windows XP. IPv4 ZeroConf Protocol: We picked the DTMC model of the IPv4 ZeroConf Protocol described in =-=[6]-=-. We next describe the model briefly without explaining its actual relation to the protocol. The DTMC model has N + 3 states: {s0,s1,...,sn,ok,err}. From the initial state s0, the system can go to two... |

3 | Black-box probabilistic verification
- Younes
- 2004
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Citation Context ...es of correctness. Both statistical approaches (presented in [21, 17]), considered a sublogic of continuous stochastic logic (CSL) that excludes steady state operator and unbounded until operator. In =-=[19]-=- the algorithm was extended to deal with a very limited class of unbounded until formulas. In particular, the algorithm in [19] cannot prove that a formula of the form P<p(true U φ) holds at a state, ... |