Confidence Bounds for Statistical Model Checking of Probabilistic Hybrid Systems

Ellen, Christian; Gerwinn, Sebastian; Fränzle, Martin

doi:10.1007/978-3-642-33365-1_10

Cited by 7 publications

(7 citation statements)

References 19 publications

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“…To construct tighter bounds, i.e., B values, also in a similar fashion to the previous section, we have to combine the confidence bounds provided by the above equations for the different operations associated with the different quantifiers, thereby propagating confidence intervals from the bottom to the root of the decision tree (forest) [7]. To this end, we state the following Lemmas.…”

Section: Updatesmentioning

confidence: 97%

“…Note that the last three quantifiers are non-random and can therefore be handled using a standard SAT modulo theory solver addressing the relevant fragment of arithmetic. In fact, analogously to [7], we evaluated this part of the formula completely, again using interval arithmetics. To this end, we have to determine the interval of potential collision speeds, which in turn amounts to calculating first and last possible points in time at which a collision could happen opting for either option (lane change or staying on the lane).…”

Section: Path Planning Use Casementioning

confidence: 99%

“…That is, in analogy to the HOO algorithm and the one presented in [7], a child is selected according to its upper and lower confidence bounds (denoted by B j h,i , B j h,i ) for existential and universal quantifiers, respectively. If there is no unique maximal (for existential quantifiers) or minimal (for universal quantifiers) branch, among the optimal branches one is selected at random (uniformly).…”

Section: Path Selection and Domain Splittingmentioning

confidence: 99%

“…In [7], we therefore extended the model checking procedure for solving SSMT problems to a more scalable version based on statistical model checking (SMC) and the upper bound confidence algorithm for trees [8]. In contrast to model checking, the SMC method generates results which can be guaranteed with a certain level of confidence only, i.e.…”

Section: Introductionmentioning

confidence: 98%

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Statistical model checking for stochastic hybrid systems involving nondeterminism over continuous domains

Ellen

Gerwinn

Fränzle

2014

Int J Softw Tools Technol Transfer

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Behavioral verification of technical systems invol ving both discrete and continuous components is a common and demanding task. The behavior of such systems can often be characterized using stochastic hybrid automata, leading to verification problems which can be formalized and solved using stochastic logic calculi such as stochastic satisfiability modulo theory (SSMT). While algorithms for discharging proof obligations in SSMT form exist, their applicability is limited due to the computational complexity, which often increases exponentially with the number of quantified variables. Recently, statistical model checking has been successfully applied to stochastic hybrid systems, thereby increasing the size of the system for which verification problems is tractable. However, being based on randomized simulation, these methods usually cannot handle non-determinism. In previous work, we have deviated from the usual approach of simulating the model and rather proposed a statistical method for SSMT solving which, being based on statistical AI planning algorithms, can also treat non-determinism over a finite domain. Here, we extend this previous work to the case of continuous domains. In particular, using ideas from noisy optimization, we adaptively build up a decision tree recording the findings and guiding further exploration, thereby favoring the currently most promising sub-domain. The non-determinism is resolved by translating the satisfac-C. Ellen (B) · S. Gerwinn Transportation, tion problem into an optimization problem, thereby computing both optimistic and pessimistic bounds on the probability of satisfaction. At each stage of the evaluation process, we show how to obtain confidence statements about the probability of satisfaction for the overall SSMT formula, including reliable estimates on the optimal resolution of any nondeterministic choice involved.

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Section: Updatesmentioning

confidence: 97%

Section: Path Planning Use Casementioning

confidence: 99%

Section: Path Selection and Domain Splittingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

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Statistical model checking for stochastic hybrid systems involving nondeterminism over continuous domains

Ellen

Gerwinn

Fränzle

2014

Int J Softw Tools Technol Transfer

Self Cite

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“…In [32], a "symbolic" search through the state space using non-probabilistic methods is performed first, after which a finite-state Markov decision process is constructed and analysed. Instead, [13,10] uses stochastic satisfiability modulo theories to permit the verification of bounded properties.…”

Section: Probabilistic Rectangular Hybrid Automatamentioning

confidence: 99%

Verification and Control of Probabilistic Rectangular Hybrid Automata

Sproston

2015

Lecture Notes in Computer Science

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Abstract. Hybrid systems are characterised by a combination of discrete and continuous components. In many application areas for hybrid systems, such as vehicular control and systems biology, stochastic behaviour is intrinsic. This has led to the development of stochastic extensions of formalisms, such as hybrid automata, for the modelling of hybrid systems, together with their associated verification and controller synthesis algorithms, in order to allow reasoning about quantitative properties such as "the vehicle's speed will reach 50kph within 10 seconds with probability at least 0.99". We consider probabilistic rectangular hybrid automata, which generalise the well-known class of rectangular hybrid automata with the possibility of representing random behavior of the discrete components of the system, permitting the modeling of the likelihood of faults, choices in randomised algorithms and message losses. We highlight the differences between verification and control problems for probabilistic rectangular hybrid automata and the corresponding problems for non-probabilistic rectangular hybrid automata. Furthermore, we will describe the effect of assumptions on the underlying model of time (discrete or continuous) on the considered verification and control problems. Finally, we will also consider how probabilistic rectangular hybrid automata can be used as abstract models for more general classes of stochastic hybrid systems.

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PAC Statistical Model Checking for Markov Decision Processes and Stochastic Games

Ashok

Křetínský

Weininger

2019

Lecture Notes in Computer Science

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Statistical model checking (SMC) is a technique for analysis of probabilistic systems that may be (partially) unknown. We present an SMC algorithm for (unbounded) reachability yielding probably approximately correct (PAC) guarantees on the results. We consider both the setting (i) with no knowledge of the transition function (with the only quantity required a bound on the minimum transition probability) and (ii) with knowledge of the topology of the underlying graph. On the one hand, it is the first algorithm for stochastic games. On the other hand, it is the first practical algorithm even for Markov decision processes. Compared to previous approaches where PAC guarantees require running times longer than the age of universe even for systems with a handful of states, our algorithm often yields reasonably precise results within minutes, not requiring the knowledge of mixing time.

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Confidence Bounds for Statistical Model Checking of Probabilistic Hybrid Systems

Cited by 7 publications

References 19 publications

Statistical model checking for stochastic hybrid systems involving nondeterminism over continuous domains

Statistical model checking for stochastic hybrid systems involving nondeterminism over continuous domains

Verification and Control of Probabilistic Rectangular Hybrid Automata

PAC Statistical Model Checking for Markov Decision Processes and Stochastic Games

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