# Model Checking Finite-Horizon Markov Chains with Probabilistic Inference

@inproceedings{Holtzen2021ModelCF, title={Model Checking Finite-Horizon Markov Chains with Probabilistic Inference}, author={Steven Holtzen and Sebastian Junges and Marcell Vazquez-Chanlatte and Todd D. Millstein and Sanjit A. Seshia and Guy Van den Broeck}, booktitle={CAV}, year={2021} }

We revisit the symbolic verification of Markov chains with respect to finite horizon reachability properties. The prevalent approach iteratively computes step-bounded state reachability probabilities. By contrast, recent advances in probabilistic inference suggest symbolically representing all horizon-length paths through the Markov chain. We ask whether this perspective advances the state-of-the-art in probabilistic model checking. First, we formally describe both approaches in order to…

## 4 Citations

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A novel static analysis technique to derive higher moments for program variables of a large class of probabilistic loops with complex control flow, polynomial assignments, symbolic constants, circular dependencies among variables, and potentially uncountable state spaces is presented.

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## References

SHOWING 1-10 OF 71 REFERENCES

The Probabilistic Model Checker Storm

- Computer ScienceInternational Journal on Software Tools for Technology Transfer
- 2021

The main features of Storm are reported and how to effectively use them are explained and an empirical evaluation of different configurations of Storm on the QComp 2019 benchmark set is presented.

Operational versus weakest pre-expectation semantics for the probabilistic guarded command language

- Computer SciencePerform. Evaluation
- 2014

On probabilistic inference by weighted model counting

- Computer ScienceArtif. Intell.
- 2008

Scaling exact inference for discrete probabilistic programs

- Computer ScienceProc. ACM Program. Lang.
- 2020

A domain-specific probabilistic programming language called Dice is developed that features a new approach to exact discrete Probabilistic program inference, and a new reduction from discrete probabilism programs to weighted model counting (WMC).

Inference and learning in probabilistic logic programs using weighted Boolean formulas

- Computer ScienceTheory and Practice of Logic Programming
- 2014

The results show that the inference algorithms improve upon the state of the art in probabilistic logic programming, and that it is indeed possible to learn the parameters of a probabilist logic program from interpretations.

Fine-Tuning the Odds in Bayesian Networks

- Computer ScienceECSQARU
- 2021

Various new analysis techniques for Bayes networks in which conditional probability tables (CPTs) may contain symbolic variables are proposed to exploit scalable and powerful techniques for synthesis problems in parametric Markov chains.

A Near-Linear-Time Algorithm for Weak Bisimilarity on Markov Chains

- Computer ScienceCONCUR
- 2020

The time bound for calculating the weak/branching bisimulation minimisation minimisation quotient on state-labelled discrete-time Markov chains is improved from O(mn) to an expected-time O(m log4 n), where n is the number of states and m thenumber of transitions.

On Correctness, Precision, and Performance in Quantitative Verification - QComp 2020 Competition Report

- Computer ScienceISoLA
- 2020

This paper surveys the precision guarantees—ranging from exact rational results to statistical confidence statements—offered by the nine participating tools and reports on the experimental evaluation of these trade-offs performed in QComp 2020: the second friendly competition of tools for the analysis of quantitative formal models.

Bayesian Inference by Symbolic Model Checking

- Computer ScienceQEST
- 2020

A simple translation from Bayesian networks into tree-like Markov chains such that inference can be reduced to computing reachability probabilities using probabilistic sentential decision diagrams and vtrees, a scalable symbolic technique in AI inference tools.

Bridging the Gap Between Probabilistic Model Checking and Probabilistic Planning: Survey, Compilations, and Empirical Comparison

- Computer ScienceJ. Artif. Intell. Res.
- 2020

The translation from Jani, an overarching input language for quantitative model checkers, into the probabilistic planning domain definition language (PPDDL), and vice versa from PPDDL into Jani are intended as a beginning to unite the two research branches.