Simple stochastic games can be solved by value iteration (VI), which yields a sequence of under-approximations of the value of the game. This sequence is guaranteed to converge to the value only in the limit. Since no stopping criterion is known, this technique does not provide any guarantees on its results. We provide the first stopping criterion for VI on simple stochastic games. It is achieved by additionally computing a convergent sequence of over-approximations of the value, relying on an analysis of the game graph. Consequently, VI becomes an anytime algorithm returning the approximation of the value and the current error bound. As another consequence, we can provide a simulationbased asynchronous VI algorithm, which yields the same guarantees, but without necessarily exploring the whole game graph. ⋆ This research was funded in part by the Studienstiftung des deutschen Volkes project "Formal methods for analysis of attack-defence diagrams", the Czech Science Foundation grant No. 18-11193S, and the German Research Foundation (DFG) project KR 4890/2-1 "Statistical Unbounded Verification". 1 Formally, the problem is to decide, for a given p ∈ [0, 1] whether Maximizer has a strategy ensuring probability at least p to reach the target.

Success or failure of attacks on high-security systems, such as hacker attacks on sensitive data, depend on various situational conditions, including the timing and success chances of single attack steps, and concurrent countermeasures of the defender. With the existing stateof-the-art modelling tools for attack scenarios, comprehensive considerations of these conditions have not been possible. This paper introduces Attack-Defence Diagrams as a formalism to describe intricate attackdefence scenarios that can represent the above mentioned situational conditions. A diagram's semantics naturally corresponds to a game where its players, the attacker and the defender, compete to turn the game's outcome from undecided into a successful attack or defence, respectively. Attack-Defence Diagrams incorporate aspects of time, probability, and cost, so as to reflect timing of attack steps and countermeasures, their success chances, as well as skills and knowledge of the attacker and defender that may increase over time with lessons learned from previous attack steps. The semantics maps on stochastic timed automata as the underlying mathematical model in a compositional manner. This enables an efficient what-if quantitative evaluation to deliver cost and success estimates, as we demonstrate by a case study from the cybersecurity domain.

In modern software development, paradigms like componentbased software engineering (CBSE) and service-oriented architectures (SOA) emphasize the construction of large software systems out of existing components or services. Therein, a service is a self-contained piece of software, which adheres to a specified interface. In a model-based software design, this interface constitutes our sole knowledge of the service at design time, while service implementations are not available. Therefore, correctness checks or detection of potential errors in service compositions has to be carried out without the possibility of executing services. This challenges the usage of standard software error localization techniques for service compositions. In this paper, we review state-of-the-art approaches for error localization of software and discuss their applicability to service compositions.

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