Symblicit algorithms for optimal strategy synthesis in monotonic Markov decision processes

When treating Markov decision processes (MDPs) with large state spaces, using explicit representations quickly becomes unfeasible. Lately, Wimmer et al. have proposed a so-called symblicit algorithm for the synthesis of optimal strategies in MDPs, in the quantitative setting of expected mean-payoff. This algorithm, based on the strategy iteration algorithm of Howard and Veinott, efficiently combines symbolic and explicit data structures, and uses binary decision diagrams as symbolic representation. The aim of this paper is to show that the new data structure of pseudo-antichains (an extension of antichains) provides another interesting alternative, especially for the class of monotonic MDPs. We design efficient pseudo-antichain based symblicit algorithms (with open source implementations) for two quantitative settings: the expected mean-payoff and the stochastic shortest path. For two practical applications coming from automated planning and LTL synthesis, we report promising experimental results w.r.t. both the run time and the memory consumption.Comment: In Proceedings SYNT 2014, arXiv:1407.493

Probabilistic Model Checking for Energy Analysis in Software Product Lines

In a software product line (SPL), a collection of software products is defined by their commonalities in terms of features rather than explicitly specifying all products one-by-one. Several verification techniques were adapted to establish temporal properties of SPLs. Symbolic and family-based model checking have been proven to be successful for tackling the combinatorial blow-up arising when reasoning about several feature combinations. However, most formal verification approaches for SPLs presented in the literature focus on the static SPLs, where the features of a product are fixed and cannot be changed during runtime. This is in contrast to dynamic SPLs, allowing to adapt feature combinations of a product dynamically after deployment. The main contribution of the paper is a compositional modeling framework for dynamic SPLs, which supports probabilistic and nondeterministic choices and allows for quantitative analysis. We specify the feature changes during runtime within an automata-based coordination component, enabling to reason over strategies how to trigger dynamic feature changes for optimizing various quantitative objectives, e.g., energy or monetary costs and reliability. For our framework there is a natural and conceptually simple translation into the input language of the prominent probabilistic model checker PRISM. This facilitates the application of PRISM's powerful symbolic engine to the operational behavior of dynamic SPLs and their family-based analysis against various quantitative queries. We demonstrate feasibility of our approach by a case study issuing an energy-aware bonding network device.Comment: 14 pages, 11 figure