The concept of features provides an elegant way to specify families of systems. Given a base system, features encapsulate additional functionalities that can be activated or deactivated to enhance or restrict the base system’s behaviors. Features can also facilitate the analysis of families of systems by exploiting commonalities of the family members and performing an all-in-one analysis, where all systems of the family are analyzed at once on a single family model instead of one-by-one. Most prominent, the concept of features has been successfully applied to describe and analyze (software) product lines. We present the tool ProFeat that supports the feature-oriented engineering process for stochastic systems by probabilistic model checking. To describe families of stochastic systems, ProFeat extends models for the prominent probabilistic model checker Prism by feature-oriented concepts, including support for probabilistic product lines with dynamic feature switches, multi-features and feature attributes. ProFeat provides a compact symbolic representation of the analysis results for each family member obtained by Prism to support, e.g., model repair or refinement during feature-oriented development. By means of several case studies we show how ProFeat eases family-based quantitative analysis and compare one-by-one and all-in-one analysis approaches.

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The paper deals with finite-state Markov decision processes (MDPs) with integer weights assigned to each state-action pair. New algorithms are presented to classify end components according to their limiting behavior with respect to the accumulated weights. These algorithms are used to provide solutions for two types of fundamental problems for integer-weighted MDPs. First, a polynomial-time algorithm for the classical stochastic shortest path problem is presented, generalizing known results for special classes of weighted MDPs. Second, qualitative probability constraints for weight-bounded (repeated) reachability conditions are addressed. Among others, it is shown that the problem to decide whether a disjunction of weight-bounded reachability conditions holds almost surely under some scheduler belongs to NP ∩ coNP, is solvable in pseudo-polynomial time and is at least as hard as solving two-player mean-payoff games, while the corresponding problem for universal quantification over schedulers is solvable in polynomial time. arXiv:1804.11301v1 [cs.LO] 30 Apr 2018 sup M,s (φ) = sup S Pr S M,s (φ) and Pr inf M,swhere S ranges over all schedulers for M. We write Pr max M,s (φ) rather than Pr sup M,s (φ) if the supremum is indeed a maximum, which is the case, e.g., if φ is an ordinary LTL formula (without weight constraints). Note that the maximum/minimum might not exist for weight-bounded properties. In any case,the extremal expectations of f , where sup and inf take values in R ∪ {−∞, +∞}, while, for instance, E max M,s (f ) will be used when the maximum exists. In particular, we will use the random variable associated with the mean payoff, defined on infinite paths by MP(ς) = lim sup n→∞ wgt(pref (ς,n)) n E T M,s (MP) ⩾ p∆ + (1−p)E c > 0, where c is the expected number of steps under T to return to s from s in normal mode. Hence, E max M (MP) > 0. □ Lemma B.9. Let M be a strongly connected MDP. Then, M is universally pumping iff E min M (MP) > 0. Pr S M,s (φ) ⩽ Pr T M i ,s (φ) ⩽ Pr S M,s (φ) + Pr S M,s ς ∈ IPaths : lim(ς) ∈ {E 1 , . . . , E i−1 } for all states s in M and all 0-EC-invariant properties φ. In particular: Pr S M,s (φ) = Pr T M i ,s (φ) if Pr S M,s {ς ∈ IPaths : lim(ς) is a 0-EC} = 0. Thus, Pr sup M,s (φ) = Pr sup M i ,s (φ) for each 0-EC-invariant property φ and each state s in M. Furthermore, the existence of a scheduler S for M with Pr sup M,s (φ) = Pr S M,s (φ) implies the existence of a scheduler T for M i with Pr sup M,s (φ) = Pr T M , s (φ), and vice versa. The proof follows from Lemma B.18 using an inductive argument. P M (s,α,s ′ ) 1−P M (s,α, E) , for each maximal weight-divergent end component F E we set P N (E out , α, F in ) = s ′ ∈ F P M (s,α,s ′ ) 1−P M (s,α, E) , and P N (E, α, E) = 0. 4 The notation P M (s, α, E) stands for the probability from s to reach any state of E. 49 Lemma D.40. Let φ be as above. Then Pr max M,s init □ (wgt ⩾ K) ∧ □ F = 1 iff Pr max M,s init (φ) = 1. Proof. The implication "⇐=" is an easy verification. Given a scheduler S with Pr S M,s init (φ) = 1, combine S w...

Probabilistic model checking (PMC) is a well-established and powerful method for the automated quantitative analysis of parallel distributed systems. Classical PMC-approaches focus on computing probabilities and expectations in Markovian models annotated with numerical values for costs and utility, such as energy and performance. Usually, the utility gained and the costs invested are dependent and a trade-off analysis is of utter interest.In this paper, we provide an overview on various kinds of nonstandard multi-objective formalisms that enable to specify and reason about the trade-off between costs and utility. In particular, we present the concepts of quantiles, conditional probabilities and expectations as well as objectives on the ratio between accumulated costs and utility. Such multi-objective properties have drawn very few attention in the context of PMC and hence, there is hardly any tool support in state-of-the-art model checkers. Furthermore, we broaden our results towards combined quantile queries, computing conditional probabilities those conditions are expressed as formulas in probabilistic computation tree logic, and the computation of ratios which can be expected on the long-run.

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