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## Bayesian Statistical Model Checking with Application to Stateflow/Simulink Verification (2010)

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Citations: | 44 - 7 self |

### Citations

1623 |
The temporal logic of programs
- Pnueli
- 1977
(Show Context)
Citation Context ...., to decide whether the modelM starting from s0 satisfies the property φ with probability at least θ. In this paper, property φ is expressed in Bounded Linear Temporal Logic (BLTL), a variant of LTL =-=[21]-=- in which the temporal operators are equipped with time bounds. Alternatively, BLTL can be viewed as a sublogic of Koymans’ Metric Temporal Logic [16, 20]. As system models M , we use a stochastic ver... |

1119 | Optimal Statistical Decisions - DeGroot - 1970 |

841 |
The Theo;;r of Probability
- Jeffreys
(Show Context)
Citation Context ...ixed priors in a given example, the Bayes factor is directly proportional to the posterior odds by (12). Thus, it may be used as a measure of relative confidence in H0 vs. H1, as proposed by Jeffreys =-=[14]-=-. To test H0 vs. H1, we compute the Bayes factor B of the available data d and then compare it against a fixed threshold T � 1: we shall accept H0 iffB > T . Jeffreys interprets the value of the Bayes... |

359 | B.: A logic for reasoning about time and reliability
- Hansson, Jonsson
- 1994
(Show Context)
Citation Context ... or whether the ignition succeeds within 1ms with probability at least 0.99. In fact, several temporal logics have been developed in order to express these and other types of probabilistic properties =-=[3, 11, 1]-=-. The Probabilistic Model Checking (PMC) problem is to decide whether a stochastic model satisfies a temporal logic property with a probability greater than or equal to a certain threshold. More forma... |

289 |
Specifying Real-Time Properties with Metric Temporal Logic
- Koymans
- 1990
(Show Context)
Citation Context ...ed Linear Temporal Logic (BLTL), a variant of LTL [19] in which the temporal operators are equipped with time bounds. Alternatively, BLTL can be viewed as a sublogic of Koymans’ Metric Temporal Logic =-=[15]-=-. As system modelsM, we use a stochastic version of hybrid systems modeled in Stateflow/Simulink. Existing algorithms for solving the PMC problem fall into one of two categories. The first category co... |

273 | 2006): PRISM: A tool for automatic verification of probabilistic systems
- Hinton, Kwiatkowska, et al.
(Show Context)
Citation Context ...gorithms for solving the PMC problem fall into one of two categories. The first category comprises numerical methods that can compute the probability that the property holds with high precision (e.g. =-=[2, 3, 5, 6, 12]-=-). Numerical methods are generally only suitable for finite-state systems of about 107 − 108 states [16]. In real control systems, the number of states easily exceeds this limit or is infinite, which ... |

230 |
Sequential tests of statistical hypotheses
- Wald
- 1945
(Show Context)
Citation Context ...m. Our initial findings suggest that the algorithm scales very well. 7 Related Work Younes and Simmons introduced the first algorithm for Statistical Model Checking [27, 28]. Their work uses the SPRT =-=[25]-=-, which is designed for simple hypothesis testing3 . Specifically, the SPRT decides between the simple null hypothesis H ′ 0 : M |= P=θ0 (φ) against the simple alternate hypothesis H ′ 1 :M |= P=θ1 (φ... |

228 | Model checking algorithms for continuous-time Markov chains
- Baier, Haverkort, et al.
- 2003
(Show Context)
Citation Context ... or whether the ignition succeeds within 1ms with probability at least 0.99. In fact, several temporal logics have been developed in order to express these and other types of probabilistic properties =-=[3, 11, 1]-=-. The Probabilistic Model Checking (PMC) problem is to decide whether a stochastic model satisfies a temporal logic property with a probability greater than or equal to a certain threshold. More forma... |

216 |
The complexity of probabilistic verification
- Courcoubetis, Yannakakis
- 1995
(Show Context)
Citation Context ...gorithms for solving the PMC problem fall into one of two categories. The first category comprises numerical methods that can compute the probability that the property holds with high precision (e.g. =-=[2, 3, 5, 6, 13]-=-). Numerical methods are generally only suitable for finite-state systems of about 10 7 − 10 8 states [17]. In real control systems, the number of states easily exceeds this limit or is infinite, whic... |

205 | The Bayesian Choice - Robert - 1994 |

123 | Probabilistic Verification of Discrete Event Systems Using Acceptance Sampling
- Younes, Simmons
- 2002
(Show Context)
Citation Context ...en compare that estimate to θ [12, 23] (in statistics such estimates are known as confidence intervals). In the second case, the PMC problem is directly treated as a hypothesis testing problem (e.g., =-=[27, 28]-=-), i.e., deciding between the hypothesis H0 :M |= P≥θ(φ) that the property holds versus the hypothesis H1 :M |= P<θ(φ) that it does not. Hypothesis-testing based methods are more efficient than those ... |

105 | D.: Model-checking for probabilistic real-time systems
- Alur, Courcoubetis, et al.
- 1991
(Show Context)
Citation Context ... or whether the ignition succeeds within 1ms with probability at least 0.99. In fact, several temporal logics have been developed in order to express these and other types of probabilistic properties =-=[3, 11, 1]-=-. The Probabilistic Model Checking (PMC) problem is to decide whether a stochastic model satisfies a temporal logic property with a probability greater than or equal to a certain threshold. More forma... |

97 | Symbolic model checking for probabilistic processes
- Baier, Clarke, et al.
- 1997
(Show Context)
Citation Context ...gorithms for solving the PMC problem fall into one of two categories. The first category comprises numerical methods that can compute the probability that the property holds with high precision (e.g. =-=[2, 3, 5, 6, 12]-=-). Numerical methods are generally only suitable for finite-state systems of about 107 − 108 states [16]. In real control systems, the number of states easily exceeds this limit or is infinite, which ... |

77 | Numerical vs. statistical probabilistic model checking: an empirical study
- Younes, Kwiatkowska, et al.
(Show Context)
Citation Context ...are more efficient than those based on estimation when θ (which is specified by the user) is significantly different from the true probability that the property holds (which is determined byM and s0) =-=[26]-=-. In this paper we show that estimation can be much faster for probabilities close to 1. Also note that Statistical Model Checking cannot guarantee a correct answer to the PMC problem. The most crucia... |

68 |
Approximate probabilistic model checking
- Hérault, Lassaigne, et al.
- 2004
(Show Context)
Citation Context ...testing. In the first case one seeks to estimate probabilistically (i.e., 1compute with high probability a value close to) the probability that the property holds and then compare that estimate to θ =-=[12, 23]-=- (in statistics such estimates are known as confidence intervals). In the second case, the PMC problem is directly treated as a hypothesis testing problem (e.g., [27, 28]), i.e., deciding between the ... |

60 | Monitoring Temporal Properties of Continuous Signals
- Maler, Nickovic
- 2004
(Show Context)
Citation Context ...r of required simulation steps expected to be finite at all? For a class of finite length continuous-time boolean signals, well-definedness of checking bounded MITL properties has been conjectured in =-=[19]-=-. Here we generalize to infinite, hybrid traces with real-valued signals. We prove well-definedness and the fact that a finite prefix of the discrete time hybrid signal is sufficient for BLTL model ch... |

58 | Monte Carlo model checking
- GROSU, SMOLKA
(Show Context)
Citation Context ... experimental results show a significant advantage of our Bayesian estimation algorithm in the sample size. Grosu and Smolka use a standard acceptance sampling technique for verifying formulas in LTL =-=[10]-=-. Their algorithm randomly samples lassos (i.e., random walks ending in a cycle) from a Büchi automaton in an on-the-fly fashion. The algorithm terminates if it finds a counterexample. Otherwise, the ... |

56 | Statistical Model Checking of Black-Box Probabilistic Systems
- Sen, Viswanathan, et al.
- 2004
(Show Context)
Citation Context ...testing. In the first case one seeks to estimate probabilistically (i.e., 1compute with high probability a value close to) the probability that the property holds and then compare that estimate to θ =-=[12, 23]-=- (in statistics such estimates are known as confidence intervals). In the second case, the PMC problem is directly treated as a hypothesis testing problem (e.g., [27, 28]), i.e., deciding between the ... |

51 | A Bayesian approach to model checking biological systems
- JHA, CLARKE, et al.
- 2009
(Show Context)
Citation Context ...r probability of p∈(t0,t1), by (10)} until (γ � c) return (t0,t1), ˆp 4 Bayesian Hypothesis Testing In this section we briefly present our sequential Bayesian hypothesis test, which was introduced in =-=[15]-=-. Let X1,...,Xn be a sequence of Bernoulli random variables defined as for the PMC problem in Sect. 3, and let d = (x1,...,xn) denote a sample of those variables. Let H0 and H1 be mutually exclusive h... |

47 | On statistical model checking of stochastic systems. See Etessami and Rajamani
- SEN, VISWANATHAN, et al.
- 2005
(Show Context)
Citation Context ...sis is true. It is important to realize that a p-value is not the probability that the null hypothesis is true. Sen et al.’s method does not have a way to control the Type I and II errors. Sen et al. =-=[24]-=- have started investigating the extension of SMC to unbounded (i.e., standard) LTL properties. Finally, Langmead [18] has applied Bayesian point estimation and SMC for querying Dynamic Bayesian Networ... |

45 | Checking Finite Traces Using Alternating Automata
- Finkbeiner, Sipma
(Show Context)
Citation Context ...emporal Logic PBLTL). We first define the syntax and semantics of Bounded Linear Temporal Logic (BLTL), which we can check on a single trace, and then extend that logic to PBLTL. Finkbeiner and Sipma =-=[8]-=- have defined a variant of LTL on finite traces of discrete-event systems (where time is thus not considered). For a stochastic modelM,let the set of state variables SV be a finite set of real-valued ... |

44 | Symmetry reduction for probabilistic model checking
- Kwiatkowska, Norman, et al.
- 2009
(Show Context)
Citation Context ...hat can compute the probability that the property holds with high precision (e.g. [2, 3, 5, 6, 13]). Numerical methods are generally only suitable for finite-state systems of about 10 7 − 10 8 states =-=[17]-=-. In real control systems, the number of states easily exceeds this limit or is infinite, which motivates the need for algorithms for solving the PMC problem in a probabilistic fashion, such as Statis... |

43 |
Statistical probabilistic model checking with a focus on time-bounded properties
- YOUNES, SIMMONS
(Show Context)
Citation Context ...en compare that estimate to θ [12, 23] (in statistics such estimates are known as confidence intervals). In the second case, the PMC problem is directly treated as a hypothesis testing problem (e.g., =-=[27, 28]-=-), i.e., deciding between the hypothesis H0 :M |= P≥θ(φ) that the property holds versus the hypothesis H1 :M |= P<θ(φ) that it does not. Hypothesis-testing based methods are more efficient than those ... |

35 | On probabilistic computation tree logic
- Ciesinski, Größer
- 2004
(Show Context)
Citation Context ...gorithms for solving the PMC problem fall into one of two categories. The first category comprises numerical methods that can compute the probability that the property holds with high precision (e.g. =-=[2, 3, 5, 6, 13]-=-). Numerical methods are generally only suitable for finite-state systems of about 10 7 − 10 8 states [17]. In real control systems, the number of states easily exceeds this limit or is infinite, whic... |

14 |
Some recent results in metric temporal logic
- Ouaknine, Worrell
- 2008
(Show Context)
Citation Context ...ed Linear Temporal Logic (BLTL), a variant of LTL [21] in which the temporal operators are equipped with time bounds. Alternatively, BLTL can be viewed as a sublogic of Koymans’ Metric Temporal Logic =-=[16, 20]-=-. As system models M , we use a stochastic version of hybrid systems modeled in Stateflow/Simulink. Existing algorithms for solving the PMC problem fall into one of two categories. The first category ... |

12 | Probabilistic plan verification through acceptance sampling
- Younes, Musliner
- 2002
(Show Context)
Citation Context ...en compare that estimate to θ [11, 21] (in statistics such estimates are known as confidence intervals). In the second case, the PMC problem is directly treated as a hypothesis testing problem (e.g., =-=[25, 26]-=-), i.e., deciding between the hypothesis H0 : M |= P≥θ(φ) that the property holds versus the hypothesis H1 :M |= P<θ(φ) that it does not. Hypothesis-testing based methods are more efficient than those... |

8 | Generalized queries and bayesian statistical model checking in dynamic bayesian networks: Application to personalized medicine
- Langmead
- 2009
(Show Context)
Citation Context ...t al.’s method does not have a way to control the Type I and II errors. Sen et al. [24] have started investigating the extension of SMC to unbounded (i.e., standard) LTL properties. Finally, Langmead =-=[18]-=- has applied Bayesian point estimation and SMC for querying Dynamic Bayesian Networks. 8 Conclusions and Future Work Extending our Statistical Model Checking (SMC) algorithm that uses Bayesian Sequent... |

6 |
A note on the limiting relative efficiency of the Wald sequential probability ratio test
- Bechhofer
- 1960
(Show Context)
Citation Context ... errors of a standard SPRT [9, Section 3.4]. However, in this case the test is no longer optimal, and the maximum expected sample size may be much bigger than the optimal fixed-size sample test - see =-=[4]-=- and [9, Section 3.6]. Our approach solves instead the composite hypothesis testing problem, with no indifference region. The method of [12] uses a fixed number of samples and estimates the probabilit... |

4 | editors. Handbook of sequential analysis - Ghosh, Sen - 1991 |

2 |
Optimal design and sequential analysis of VLSI testing strategy
- Yu, Krishna, et al.
- 1988
(Show Context)
Citation Context ...ion: number of samples vs probability that it is not currently matched by other SMC estimation techniques (e.g., [12]). Our findings are consistent with those of Yu et al. for the VLSI testing domain =-=[29]-=-. Our simulations also indicate that the performance of the algorithm depends more strongly on the half-size δ of the estimated interval than on the coverage c of the interval itself. It is much faste... |