The 10,000 Facets of MDP Model Checking

Abstract

This paper presents a retrospective view on probabilistic model checking. We focus on Markov decision processes (MDPs, for short). We survey the basic ingredients of MDP model checking and discuss its enormous developments since the seminal works by Courcoubetis and Yannakakis in the early 1990s. We discuss in particular the manifold facets of this field of research by surveying the verification of various MDP extensions, rich classes of properties, and their applications.

Methods, Languages and Tools for Future System Development

“…The 10,000 Facets of MDP Model Checking [2] presents how probabilistic model checking can be applied to Markov Decision Processes (MDP), which have a wide range of application areas ranging from stochastic and dynamic optimization problems to robotics. Given an MDP and a property φ written in some probabilistic logic, MDP model checking fully automatically determines all states of the MDP that satisfy property φ.…”

“…Technical progress does not necessarily mean conceptual improvement, as summarized by Dijkstra [9]: "as long as there were no machines, programming was no problem at all; when we had a few weak computers, programming became a mild problem, and now we have gigantic computers, 1 programming has become an equally gigantic problem". This quote from 1972, which expresses Dijkstra's frustration in having to deal with increasingly powerful, but also increasingly difficult-to-handle machinery, embodies an important message to software scientists, the quest for simplicity 2 , a message even more important today.…”

Language-Driven Engineering: From General-Purpose to Purpose-Specific Languages

“…They provide means to automatically generate domain-specific graphical views for textual DSLs realized in the Eclipse modeling context. 19 We therefore concentrate on graphical DSLs in this subsection. Prominent frameworks for the development of graphical modeling languages are MetaEdit+ [9,55], GME [12,64,65], Pounamu/Marama [8,39,108] or DeVIL [54,88].…”

“…Also the approaches presented in the remaining papers could profit from DSLs, e.g., as follows: [41] for specifying certain assertions or contracts, [43] for specifying data flow analyses 20 , [25] for specifying test models, [42] for defining learning alphabets or representing the learning result, [40] for modularly specifying the required code instrumentation, e.g. in an aspect-oriented fashion, and [15,19,66] for conveniently specifying their enriched system structures. Corresponding mIDEs (could) then guide the development by exploiting the DSL's specifics, e.g., the interpretation of assertions, security predicates, time, or probabilities.…”

“…On the other hand, LDE could also profit from the approaches presented in the other papers. In particular, all the involved analysis, verification and validation methods of [15,19,25,[40][41][42][43]61,66] are good candidates for inclusion in mIDEs in order to improve the development support and/or to control nonfunctional constraints. Finally, [27] provides a wealth of observations and techniques with potential to impact the future mIDE development.…”