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A Compositional Semantics of Boolean-Logic Driven Markov Processes
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DOI：10.1109/TDSC.2023.3261270.png)
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Abstract
En 中文
Boolean-logic driven Markov processes (BDMPs) is a prominent dynamic extension of static fault trees to model repairable and complex dynamic systems. While BDMPs are intensively used in an industrial context for dependability analysis of energy systems, its formal semantics has not been systematically treated. To date, BDMPs are defined as a library of the domain-specific dependability-modelling language Figaro, which is neither open source nor publicly available. A rigorous semantic underpinning of BDMPs is indispensable for (1) developing BDMP analysis tools and (2) comparing its expressive power to other related reliability modelling languages. This paper presents a formal semantics to BDMPs using Markov automata (MA), an extension of continuous-time Markov chains (CTMCs) with action transitions to compose complex MA from smaller MA. This enables us to provide a compositional semantics. That is, we express the semantics of each individual BDMP element as an MA and obtain the MA for the entire BDMP by combining the MA of its elements. This makes the semantics comprehensible, for those familiar with automata theory, and easily extensible with new BDMP elements, e.g., to model security aspects. After considering the entire BDMP, the actions in its MA that were used to glue the MA of BDMP elements are ignored. This results in a CTMC amenable to exact numerical analysis by, e.g., efficient probabilistic model-checking techniques. We report on a prototypical implementation of our semantics and empirically show that our semantics yields dependability metrics that correspond to the interpretation by the Figaro knowledge base of BDMPs.
Keywords:
Boolean-logic driven markov processes
dependability analysis
fault trees
formal methods
markov automata
probabilistic model checking
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