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…
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References
SHOWING 1-10 OF 47 REFERENCES
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.
Faster algorithms for quantitative verification in bounded treewidth graphs
- Computer ScienceFormal Methods in System Design
- 2021
We consider 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…
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
D-Width: A More Natural Measure for Directed Tree Width
- Computer ScienceMFCS
- 2005
A new simple definition for directed tree-width is proposed and a special case of the min-max theorem (duality theorem) relating haven order, bramble number, and tree- width on digraphs is proved.