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… 

Figures and Tables from this paper

References

SHOWING 1-10 OF 47 REFERENCES

Faster algorithms for quantitative verification in bounded treewidth graphs

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

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

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

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

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.

On tree-partition-width

  • D. Wood
  • Mathematics, Computer Science
    Eur. J. Comb.
  • 2009

Counterexamples in Probabilistic Model Checking

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

The Treewidth of Java Programs

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