Automatic Verification of Competitive Stochastic Systems

Abstract

Abstract. We present automatic verification techniques for the modelling and analysis of probabilistic systems that incorporate competitive behaviour. These systems are modelled as turn-based stochastic multiplayer games, in which the players can either collaborate or compete in order to achieve a particular goal. We define a temporal logic called rPATL for expressing quantitative properties of stochastic multi-player games. This logic allows us to reason about the collective ability of a set of players to achieve a goal relating to the probability of an event's occurrence or the expected amount of cost/reward accumulated. We give a model checking algorithm for verifying properties expressed in this logic and implement the techniques in a probabilistic model checker, based on the PRISM tool. We demonstrate the applicability and efficiency of our methods by deploying them to analyse and detect potential weaknesses in a variety of large case studies, including algorithms for energy management and collective decision making for autonomous systems.

Stochastic game analysis and latency awareness for proactive self-adaptation

“…Intuitively, if there is no cost associated with adaptation, a reactive approach could adapt at the time a condition requiring adaptation is detected without any negative consequence. In their work, Poladian et 4 See [6] for more details on SMG strategy synthesis. al.…”

“…The choices in the environment module are specified non-deterministically to obtain a representative specification of the environment (through strategy synthesis) that is not limited to specific behaviors, since this would limit the generality of our analysis. Listing 2 shows the encoding used for the environment, in which Lines 1-3 define different constants that parameterize its behavior: 6 • MAX TIME defines the time frame for the system's execution in the model ([0,MAX TIME]). • TAU sets time granularity, defining the frequency with which the environment updates the value of non-controllable variables, and the system responds to these changes.…”

“…Our approach to analyzing adaptation builds upon a recent technique for modeling and analyzing SMGs [6]. In this approach, systems are modeled as turn-based SMGs, meaning that in each state of the model, only one player can choose between several actions, the outcome of which can be probabilistic.…”

“…Actions enlist trigger, enlist, and discharge are explicitly labeled to improve readability (see Listing 3), but are still asynchronous in our model 6. Constant values not defined in the model are provided as command-line input parameters to the tool.…”

Optimal planning for architecture-based self-adaptation via model checking of stochastic games

“…In this paper, we contribute a novel approach to automatically synthesize optimal reactive adaptation plans via model checking of stochastic multiplayer games (SMGs) [6] that enables: (i) trade-off analysis among different qualities by means of utility functions and preferences, and (ii) modeling of uncertainty both as probabilistic outcomes of adaptation actions and through explicit modeling of the behavior of the system's environment.…”