Model Checking Finite-Horizon Markov Chains with Probabilistic Inference

Holtzen, Steven; Junges, Sebastian; Vazquez-Chanlatte, Marcell; Millstein, Todd; Seshia, Sanjit A.; Broeck, Guy Van den

doi:10.1007/978-3-030-81688-9_27

Cited by 11 publications

(5 citation statements)

References 53 publications

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“…This is in line with our findings on comparing MTBDD versus PSDD Shih et al (2018). take a different approach and directly use BDD-based techniques to formally verify BN classifiers Holtzen et al (2021). take a reverse approach: they investigate to what extent recent advances in probabilistic inference can be used to accelerate PMC of finite-horizon objectives (i.e., reachability within a given number of steps).…”

supporting

confidence: 73%

Automatically Finding the Right Probabilities in Bayesian Networks

Salmani,

Katoen

2023

jair

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This paper presents alternative techniques for inference on classical Bayesian networks in which all probabilities are fixed, and for synthesis problems when conditional probability tables (CPTs) in such networks contain symbolic parameters rather than concrete probabilities. The key idea is to exploit probabilistic model checking as well as its recent extension to parameter synthesis techniques for parametric Markov chains. To enable this, the Bayesian networks are transformed into Markov chains and their objectives are mapped onto probabilistic temporal logic formulas. For exact inference, we compare probabilistic model checking to weighted model counting on various Bayesian network benchmarks. We contrast symbolic model checking using multi-terminal binary (aka: algebraic) decision diagrams to symbolic inference using proba- bilistic sentential decision diagrams, symbolic data structures that are tailored to Bayesian networks. For the parametric setting, we describe how our techniques can be used for various synthesis problems such as computing sensitivity functions (and values), simple and difference parameter tuning and ratio parameter tuning. Our parameter synthesis techniques are applicable to arbitrarily many, possibly dependent, parameters that may occur in multiple CPTs. This lifts restrictions, e.g., on the number of parametrized CPTs, or on parameter dependencies between several CPTs, that exist in the literature. Experiments on several benchmarks show that our parameter synthesis techniques can treat parameter synthesis for Bayesian networks (with hundreds of unknown parameters) that are out of reach for existing techniques.

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supporting

confidence: 73%

Automatically Finding the Right Probabilities in Bayesian Networks

Salmani,

Katoen

2023

jair

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“…Recent work [72,73] shows that ideas and methods for parameter synthesis in Markov chains as described in this survey significantly improve upon existing methods for parametric Bayesian networks [21]. Vice versa, some inference techniques do yield interesting alternatives for the analysis of (finite-horizon properties in) pMCs [46].…”

Section: Epiloguementioning

confidence: 95%

Parameter Synthesis in Markov Models: A Gentle Survey

Jansen¹,

Junges²,

Katoen³

2022

Lecture Notes in Computer Science

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This paper surveys the analysis of parametric Markov models whose transitions are labelled with functions over a finite set of parameters. These models are symbolic representations of uncountable many concrete probabilistic models, each obtained by instantiating the parameters. We consider various analysis problems for a given logical specification ϕ: do all parameter instantiations within a given region of parameter values satisfy ϕ?, which instantiations satisfy ϕ and which ones do not?, and how can all such instantiations be characterised, either exactly or approximately? We address theoretical complexity results and describe the main ideas underlying state-of-the-art algorithms that established an impressive leap over the last decade enabling the fully automated analysis of models with millions of states and thousands of parameters.

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“…Symbolic Inference. Probabilistic inference -in the finite-horizon case -employs weighted model counting via either decision diagrams annotated with probabilities as in Dice [41,40] or approximate versions by SAT/SMT-solvers [21,22,27,54,17]. PSI [35] determines symbolic representations of exact distributions.…”

Section: Related Workmentioning

confidence: 99%

Probabilistic Program Verification via Inductive Synthesis of Inductive Invariants

Batz

Chen

Junges

et al. 2023

Tools and Algorithms for the Construction and Analysis of Systems

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Essential tasks for the verification of probabilistic programs include bounding expected outcomes and proving termination in finite expected runtime. We contribute a simple yet effective inductive synthesis approach for proving such quantitative reachability properties by generating inductive invariants on source-code level. Our implementation shows promise: It finds invariants for (in)finite-state programs, can beat state-of-the-art probabilistic model checkers, and is competitive with modern tools dedicated to invariant synthesis and expected runtime reasoning.

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Model Checking Finite-Horizon Markov Chains with Probabilistic Inference

Cited by 11 publications

References 53 publications

Automatically Finding the Right Probabilities in Bayesian Networks

Automatically Finding the Right Probabilities in Bayesian Networks

Parameter Synthesis in Markov Models: A Gentle Survey

Probabilistic Program Verification via Inductive Synthesis of Inductive Invariants

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