# Witnessing subsystems for probabilistic systems with low tree width

@article{Jantsch2021WitnessingSF, title={Witnessing subsystems for probabilistic systems with low tree width}, author={Simon Jantsch and Jakob Piribauer and Christel Baier}, journal={ArXiv}, year={2021}, volume={abs/2109.08326} }

A standard way of justifying that a certain probabilistic property holds in a system is to provide a witnessing subsystem (also called critical subsystem) for the property. Computing minimal witnessing subsystems is NP-hard already for acyclic Markov chains, but can be done in polynomial time for Markov chains whose underlying graph is a tree. This paper considers the problem for probabilistic systems that are similar to trees or paths. It introduces the parameters directed tree-partition width…

## References

SHOWING 1-10 OF 47 REFERENCES

### Faster algorithms for quantitative verification in bounded treewidth graphs

- Computer ScienceFormal Methods Syst. Des.
- 2021

This work considers the core algorithmic problems related to verification of systems with respect to three classical quantitative properties, namely, the mean-payoff, the ratio, and the minimum initial credit for energy property, and presents an algorithm that approximates themean- payoff value within a factor of 1+ in time O(n · log(n/ )) as compared to the classical exact algorithms on general graphs that require quadratic time.

### Faster Algorithms for Markov Decision Processes with Low Treewidth

- Computer Science, MathematicsCAV
- 2013

Two improved static algorithms are presented for both the maximal end-component decomposition and the almost-sure reachability set computation for Markov decision processes (MDPs) for MDPs with treewidth k that run in amortized logarithmic time.

### Faster Algorithms for Quantitative Analysis of MCs and MDPs with Small Treewidth

- Computer ScienceATVA
- 2020

It is shown that treewidth can also be used to obtain faster algorithms for the quantitative problems, and that on low-treewidth MCs and MDPs, new algorithms outperform existing well-established methods by one or more orders of magnitude.

### Farkas Certificates and Minimal Witnesses for Probabilistic Reachability Constraints

- Computer ScienceTACAS
- 2020

Farkas certificates for lower and upper bounds on minimal and maximal reachability probabilities in Markov decision processes (MDP) are introduced using an MDP-variant of Farkas’ Lemma.

### Switss: Computing Small Witnessing Subsystems

- Computer Science2020 Formal Methods in Computer Aided Design (FMCAD)
- 2020

Switss is presented, a tool for the computation of Small WITnessing SubSystems that implements exact and heuristic approaches based on reducing the problem to (mixed integer) linear programming.

### Counterexamples in Probabilistic Model Checking

- Computer Science, MathematicsTACAS
- 2007

This paper considers algorithms for counterexample generation for (bounded) probabilistic reachability properties in fully Probabilistic systems and adopts (partially new) k shortest paths algorithms that dynamically determine k.

### Minimal counterexamples for linear-time probabilistic verification

- Computer Science, MathematicsTheor. Comput. Sci.
- 2014

### The Treewidth of Java Programs

- Computer ScienceALENEX
- 2002

It is shown that even if Java does not have a goto, the labelled break and continue statements are in a sense equally bad, and can be used to construct Java programs that are arbitrarily hard to understand and optimize, boding well for the application of treewidth to compiler optimization.

### On the complexity of finding balanced oneway cuts

- Mathematics, Computer ScienceInf. Process. Lett.
- 2003