Probabilistic causes in Markov Chains

Research output: Contribution to journalResearch articleContributedpeer-review


By combining two of the central paradigms of causality, namely counterfactual reasoning and probability-raising, we introduce a probabilistic notion of cause in Markov chains. Such a cause consists of finite executions of the probabilistic system after which the probability of an ω-regular effect exceeds a given threshold. The cause, as a set of executions, then has to cover all behaviors exhibiting the effect. With these properties, such causes can be used for monitoring purposes where the aim is to detect faulty behavior before it actually occurs. In order to choose which cause should be computed, we introduce multiple types of costs to capture the consumption of resources by the system or monitor from different perspectives, and study the complexity of computing cost-minimal causes.


Original languageEnglish
Pages (from-to)347-367
Number of pages21
JournalInnovations in Systems and Software Engineering
Issue number3
Publication statusPublished - 25 Apr 2022

External IDs

Scopus 85128827096
unpaywall 10.1007/s11334-022-00452-8
dblp journals/isse/ZiemekPFJB22
WOS 000787142300001
Mendeley dc884727-a7c0-39bc-991f-344fa54713df
ORCID /0000-0002-5321-9343/work/142236695
ORCID /0000-0002-8490-1433/work/142246189


DFG Classification of Subject Areas according to Review Boards

Subject groups, research areas, subject areas according to Destatis

ASJC Scopus subject areas


  • Causality, Expected costs, Markov chain, Model checking