Parameter Synthesis for Markov Models

Junges, Sebastian; Ábrahám, Erika; Hensel, Christian; Jansen, Nils; Katoen, Joost-Pieter; Quatmann, Tim; Volk, Matthias

doi:10.48550/arxiv.1903.07993

Cited by 6 publications

(12 citation statements)

References 96 publications

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“…Parametric model checkers including PARAM [13] and PROPhESY [9] are able to determine these probabilities for parametric DTMCs with respect to a given PCTL by solving the symbolic solution function synthesis problem [4,13,22,23].…”

Section: Computing Property Satisfaction Probabilitiesmentioning

confidence: 99%

“…al, who provided theoretical assurances for pDTMCs with 1-2 parameters, and Daws, who provides a stateelimination algorithm for pDTMCs with non-nested PCTL properties [4,38]. More recent methods have been developed to improve this computation, and these techniques have been implemented in tools such as PARAM, Prism, Storm, and PROPhESY [9,10,12,13,18,40,41].…”

Section: Related Workmentioning

confidence: 99%

“…Another related area of study is in parameter synthesis for pDTMCs [7][8][9][10][11]. The parameter synthesis problem takes a pDTMC and temporal logic property, and attempts to partition the parameter space into accepting and non-accepting regions.…”

Section: Related Workmentioning

confidence: 99%

“…Early work in this area primarily concerned reachability properties, and could only handle small parameter spaces [7][8][9]. In the past few years, new approaches have improved these methods to handle larger parameter spaces and more PCTL properties [10,11].…”

Section: Related Workmentioning

confidence: 99%

“…The majority of these works focus on uncertainty in models with small parameter spaces, considering only a limited set of properties [7][8][9]. In the past few years, improvements have been made to these techniques making probabilistic model checking in the presence of uncertainty more feasible for large-scale systems with many uncertainties [10,11]. However, most existing work considers only non-adversarial uncertainty, and does not account for situations in which an adversary may gain control of certain system components in order to intentionally reduce utility of the system.…”

Section: Introductionmentioning

confidence: 99%

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Adversarial Robustness Verification and Attack Synthesis in Stochastic Systems

Oakley¹,

Oprea²,

Tripakis³

2021

Preprint

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Probabilistic model checking is a useful technique for specifying and verifying properties of stochastic systems including randomized protocols and the theoretical underpinnings of reinforcement learning models. However, these methods rely on the assumed structure and probabilities of certain system transitions. These assumptions may be incorrect, and may even be violated in the event that an adversary gains control of some or all components in the system.In this paper, motivated by research in adversarial machine learning on adversarial examples, we develop a formal framework for adversarial robustness in systems defined as discrete time Markov chains (DTMCs). We base our framework on existing probabilistic verification frameworks for probabilistic temporal logic properties. We also extend our framework to include deterministic, memoryless policies acting in Markov decision processes (MDPs). Our framework includes a flexible approach for specifying several adversarial models with different capabilities to manipulate the system. We outline a class of threat models under which adversaries can perturb system transitions, constrained by an ε ball around the original transition probabilities and define four specific instances of this threat model. Notably, we consider the situation where the adversary can only modify transitions which existed in the original DTMC, as well as the more powerful case where the adversary can modify the structure of the DTMC by adding transitions.We define three main DTMC adversarial robustness problems: adversarial robustness verification, maximal δ synthesis, and worst case attack synthesis. We present two optimizationbased solutions to these three problems, leveraging traditional and parametric probabilistic model checking techniques. We then evaluate our solutions on two stochastic protocols and a collection of GridWorld case studies, which model an agent acting in an environment described as an MDP. We find that the parametric solution results in fast computation for small parameter spaces. In the case of less restrictive (stronger) adversaries, the number of parameters increases, and directly computing property satisfaction probabilities is more scalable. We demonstrate the usefulness of our definitions and solutions by comparing system outcomes over various properties, threat models, and case studies.

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Section: Computing Property Satisfaction Probabilitiesmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Adversarial Robustness Verification and Attack Synthesis in Stochastic Systems

Oakley¹,

Oprea²,

Tripakis³

2021

Preprint

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$$\textsf{PFL}$$: A Probabilistic Logic for Fault Trees

Nicoletti

Lopuhaä-Zwakenberg

Hahn

et al. 2023

Lecture Notes in Computer Science

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Safety-critical infrastructures must operate in a safe and reliable way. Fault tree analysis is a widespread method used for risk assessment of these systems: fault trees (FTs) are required by, e.g., the Federal Aviation Administration and the Nuclear Regulatory Commission. In spite of their popularity, little work has been done on formulating structural queries about FT and analyzing these, e.g., when evaluating potential scenarios, and to give practitioners instruments to formulate queries on fts in an understandable yet powerful way. In this paper, we aim to fill this gap by extending BFL [32], a logic that reasons about Boolean fts. To do so, we introduce a Probabilistic Fault tree Logic (PFL). PFL is a simple, yet expressive logic that supports easier formulation of complex scenarios and specification of FT properties that comprise probabilities. Alongside PFL, we present LangPFL, a domain specific language to further ease property specification. We showcase PFL and LangPFL by applying them to a COVID-19 related FT and to a FT for an oil/gas pipeline. Finally, we present theory and model checking algorithms based on binary decision diagrams (BDDs).

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Scenario-based verification of uncertain parametric MDPs

Badings

Cubuktepe

Jansen

et al. 2022

Int J Softw Tools Technol Transfer

Self Cite

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We consider parametric Markov decision processes (pMDPs) that are augmented with unknown probability distributions over parameter values. The problem is to compute the probability to satisfy a temporal logic specification with any concrete MDP that corresponds to a sample from these distributions. As solving this problem precisely is infeasible, we resort to sampling techniques that exploit the so-called scenario approach. Based on a finite number of samples of the parameters, the proposed method yields high-confidence bounds on the probability of satisfying the specification. The number of samples required to obtain a high confidence on these bounds is independent of the number of states and the number of random parameters. Experiments on a large set of benchmarks show that several thousand samples suffice to obtain tight and high-confidence lower and upper bounds on the satisfaction probability.

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Parameter Synthesis for Markov Models

Cited by 6 publications

References 96 publications

Adversarial Robustness Verification and Attack Synthesis in Stochastic Systems

Adversarial Robustness Verification and Attack Synthesis in Stochastic Systems

$$\textsf{PFL}$$: A Probabilistic Logic for Fault Trees

Scenario-based verification of uncertain parametric MDPs

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