“…On the other hand, quantitative verication or probabilistic model checking [13,23,38] can analyze quantitative guarantees of systems (e.g., on performance, reliability) under uncertainty, but use notations (e.g., PRISM [39], PEPA [27], cpGCL [34]) that do not retain the exibility in describing structures of relational methods. Recent product line reliability analysis approaches [16,17,26,41] improve on exibility by introducing systematic treatment of variability, but are not equipped to synthesize or explore complex structures, and lack languages tailored to check sophisticated properties across design spaces (i.e., temporal logics employed like PCTL [38] can capture properties only about a single model, not collections of individual variants). Other works in quantitative optimization of architectures [3,6,8,10,11,21,22,29,44,45] can in some cases synthesize complex structures [6,21], but are not compatible with formal verication and can only provide estimates of probabilistic properties that could dier from actual guarantees (e.g., worst case) available only via exhaustive state-space exploration.…”