Comparison of Algorithms for Simple Stochastic Games (Full Version)

Simple stochastic games are turn-based 2.5-player zero-sum graph games with a reachability objective. The problem is to compute the winning probability as well as the optimal strategies of both players. In this paper, we compare the three known classes of algorithms -- value iteration, strategy iteration and quadratic programming -- both theoretically and practically. Further, we suggest several improvements for all algorithms, including the first approach based on quadratic programming that avoids transforming the stochastic game to a stopping one. Our extensive experiments show that these improvements can lead to significant speed-ups. We implemented all algorithms in PRISM-games 3.0, thereby providing the first implementation of quadratic programming for solving simple stochastic games

Probabilistic model-checking of collaborative robots: a human injury assessment in agricultural applications

Current technology has made it possible to automate a number of agricultural processes that were traditionally carried out by humans and now can be entirely performed by robotic platforms. However, there are certain tasks like soft fruit harvesting, where human skills are still required. In this case, the robot's job is to cooperate/collaborate with human workers to alleviate their physical workload and improve the harvesting efficiency. To accomplish that in a safe and reliable way, the robot should incorporate a safety system whose main goal is to reduce the risk of harming human co-workers during close human-robot interaction (HRI). In this context, this paper presents a theoretical study, addressing the safety risks of using collaborative robots in agricultural scenarios, especially in HRI situations when the robot's safety system is not completely reliable and a component may fail. The agricultural scenarios discussed in this paper include automatic harvesting, logistics operations, crop monitoring, and plant treatment using UV-C light. A human injury assessment is conducted based on converting the HRI in each agricultural scenario into a formal mathematical representation. This representation is later implemented in a probabilistic model-checking tool. We then use this tool to perform a sensitivity analysis that allows us to determine the probability that a human may get injured according to the occurrence of failures in the robot's safety system. The probabilistic modeling methodology presented in this work can be used by safety engineers as a guideline to construct their own HRI models and then use the results of the model-checking to enhance the safety and reliability of their robot's safety system architectures

PRISM-games 3.0: Stochastic Game Verification with Concurrency, Equilibria and Time

We present a major new release of the PRISM-games model checker, featuring multiple significant advances in its support for verification and strategy synthesis of stochastic games. Firstly, concurrent stochastic games bring more realistic modelling of agents interacting in a concurrent fashion. Secondly, equilibria-based properties provide a means to analyse games in which competing or collaborating players are driven by distinct objectives. Thirdly, a real-time extension of (turn-based) stochastic games facilitates verification and strategy synthesis for systems where timing is a crucial aspect. This paper describes the advances made in the tool’s modelling language, property specification language and model checking engines in order to implement this new functionality. We also summarise the performance and scalability of the tool, and describe a selection of case studies, ranging from security protocols to robot coordination, which highlight the benefits of the new features

PRISM-games 3.0: Stochastic game verification with concurrency, equilibria and time

We present a major new release of the PRISM-games model checker, featuring multiple significant advances in its support for verification and strategy synthesis of stochastic games. Firstly, concurrent stochastic games bring more realistic modelling of agents interacting in a concurrent fashion. Secondly, equilibria-based properties provide a means to analyse games in which competing or collaborating players are driven by distinct objectives. Thirdly, a real-time extension of (turn-based) stochastic games facilitates verification and strategy synthesis for systems where timing is a crucial aspect. This paper describes the advances made in the tool’s modelling language, property specification language and model checking engines in order to implement this new functionality. We also summarise the performance and scalability of the tool, and describe a selection of case studies, ranging from security protocols to robot coordination, which highlight the benefits of the new features

Automatic Verification of Concurrent Stochastic Systems

Automated verification techniques for stochastic games allow formal reasoning about systems that feature competitive or collaborative behaviour among rational agents in uncertain or probabilistic settings. Existing tools and techniques focus on turn-based games, where each state of the game is controlled by a single player, and on zero-sum properties, where two players or coalitions have directly opposing objectives. In this paper, we present automated verification techniques for concurrent stochastic games (CSGs), which provide a more natural model of concurrent decision making and interaction. We also consider (social welfare) Nash equilibria, to formally identify scenarios where two players or coalitions with distinct goals can collaborate to optimise their joint performance. We propose an extension of the temporal logic rPATL for specifying quantitative properties in this setting and present corresponding algorithms for verification and strategy synthesis for a variant of stopping games. For finite-horizon properties the computation is exact, while for infinite-horizon it is approximate using value iteration. For zero-sum properties it requires solving matrix games via linear programming, and for equilibria-based properties we find social welfare or social cost Nash equilibria of bimatrix games via the method of labelled polytopes through an SMT encoding. We implement this approach in PRISM-games, which required extending the tool's modelling language for CSGs, and apply it to case studies from domains including robotics, computer security and computer networks, explicitly demonstrating the benefits of both CSGs and equilibria-based properties

Automatic verification of concurrent stochastic systems

Automated verification techniques for stochastic games allow formal reasoning about systems that feature competitive or collaborative behaviour among rational agents in uncertain or probabilistic settings. Existing tools and techniques focus on turn-based games, where each state of the game is controlled by a single player, and on zero-sum properties, where two players or coalitions have directly opposing objectives. In this paper, we present automated verification techniques for concurrent stochastic games (CSGs), which provide a more natural model of concurrent decision making and interaction. We also consider (social welfare) Nash equilibria, to formally identify scenarios where two players or coalitions with distinct goals can collaborate to optimise their joint performance. We propose an extension of the temporal logic rPATL for specifying quantitative properties in this setting and present corresponding algorithms for verification and strategy synthesis for a variant of stopping games. For finite-horizon properties the computation is exact, while for infinite-horizon it is approximate using value iteration. For zero-sum properties it requires solving matrix games via linear programming, and for equilibria-based properties we find social welfare or social cost Nash equilibria of bimatrix games via the method of labelled polytopes through an SMT encoding. We implement this approach in PRISM-games, which required extending the tool’s modelling language for CSGs, and apply it to case studies from domains including robotics, computer security and computer networks, explicitly demonstrating the benefits of both CSGs and equilibria-based properties