Periodic Reporting for period 2 - ForM-SMArt (Formal Methods for Stochastic Models: Algorithms and Applications)
Periodo di rendicontazione: 2022-07-01 al 2023-12-31
• The problem considered in this project is to develop faster algorithmic approaches for formal analysis of stochastic systems.
• Stochastic systems arise in several practical applications, e.g. randomized algorithms, evolutionary dynamics, design of stochastic protocols, systems in uncertain environments, to name a few. Formal analysis of such systems is necessary to develop robust systems with guarantees so that they can be deployed in safety-critical applications. Thus analysis of stochastic systems has deep impact for the society.
• The overall objectives of the project is to develop algorithmic approaches for finite-state and infinite-state stochastic games, stochastic evolutionary dynamics of games, and their applications in different domains.
• Stochastic systems arise in several practical applications, e.g. randomized algorithms, evolutionary dynamics, design of stochastic protocols, systems in uncertain environments, to name a few. Formal analysis of such systems is necessary to develop robust systems with guarantees so that they can be deployed in safety-critical applications. Thus analysis of stochastic systems has deep impact for the society.
• The overall objectives of the project is to develop algorithmic approaches for finite-state and infinite-state stochastic games, stochastic evolutionary dynamics of games, and their applications in different domains.
We have made significant progress since the start of the project. In particular, in each of the four aims we have obtained important results. In the first aim for finite-state stochastic models, we achieved faster symbolic algorithms, established non-trivial conditional lower bounds, and presented the first sub-exponential algorithm that breaks a long-standing barrier. For the second aim for infinite-state stochastic models, we presented a sound and complete approach to obtain quantitative bounds for termination of probabilistic programs, and developed new approaches for assertion-violation and non-termination. For the third aim on evolutionary games, we presented a unifying framework for two different fields of game theory, as well as presented methods that allow for emergence of cooperative behavior in the absence of perfect information. Finally, in the fourth aim for applications, we have shown that the algorithmic approaches developed have many applications, such as, stability analysis of control system and safety verification of Bayesian neural networks
We achieved several important progress beyond the state of the art. In the first aim we obtain new algorithms that break the long-standing barrier. In the second aim, for a fundamental problem we present the first sound and complete approach. In the third aim, we present the first unifying framework to study different aspects of game theory. All these results are important developments beyond the state of the art. Moreover, all of these present interesting directions to explore. First, whether our new algorithmic approaches lead to better bounds for other related problems, e.g. risk-aware analysis of stochastic system. Second, whether efficient and practical automated tools can be developed using our sound and complete methods. Third, can we (a) consider other aspects of partial information, e.g. about the environment, in evolutionary dynamics in stochastic games, and (b)resolve some of the open computational complexity results. We believe by then end of the project we will be able to answer some of these fascinating questions and thus achieve significant progress beyond the state of the art.