Witnessing subsystems for probabilistic systems with low tree width release_3uwe4jxcfve73lwzn3mw4sttca

by Simon Jantsch, Jakob Piribauer, Christel Baier

Released as a article .

2021  

Abstract

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 (dtpw) and directed path-partition width (dppw) and shows that computing minimal witnesses remains NP-hard for Markov chains with bounded dppw (and hence also for Markov chains with bounded dtpw). By observing that graphs of bounded dtpw have bounded width with respect to all known tree similarity measures for directed graphs, the hardness result carries over to these other tree similarity measures. Technically, the reduction proceeds via the conceptually simpler matrix-pair chain problem, which is introduced and shown to be NP-complete for nonnegative matrices of fixed dimension. Furthermore, an algorithm which aims to utilise a given directed tree partition of the system to compute a minimal witnessing subsystem is described. It enumerates partial subsystems for the blocks of the partition along the tree order, and keeps only necessary ones. A preliminary experimental analysis shows that it outperforms other approaches on certain benchmarks which have directed tree partitions of small width.
In text/plain format

Archived Files and Locations

application/pdf  688.0 kB
file_f27kgmoldvh4lb4hgoa6zbi72e
arxiv.org (repository)
web.archive.org (webarchive)
Read Archived PDF
Preserved and Accessible
Type  article
Stage   submitted
Date   2021-08-18
Version   v1
Language   en ?
arXiv  2108.08070v1
Work Entity
access all versions, variants, and formats of this works (eg, pre-prints)
Catalog Record
Revision: e3dc6565-a4e7-48c3-bce5-30ca831b4aa6
API URL: JSON