Formal Methods for Stochastic Models: Algorithms and Applications

Informazioni relative al progetto

ForM-SMArt

ID dell’accordo di sovvenzione: 863818

DOI

10.3030/863818

Progetto chiuso

Data della firma CE 22 Gennaio 2020

Data di avvio 1 Gennaio 2021

Data di completamento 31 Dicembre 2025

Finanziato da

• EXCELLENT SCIENCE - European Research Council (ERC)

Costo totale

€ 1 997 918,00

Contributo UE

€ 1 997 918,00

Coordinato da

INSTITUTE OF SCIENCE AND TECHNOLOGY AUSTRIA
Austria

Periodic Reporting for period 4 - ForM-SMArt (Formal Methods for Stochastic Models: Algorithms and Applications)

Periodo di rendicontazione: 2025-07-01 al 2025-12-31

Sintesi del contesto e degli obiettivi generali del progetto

• 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.

Lavoro eseguito dall’inizio del progetto fino alla fine del periodo coperto dalla relazione e principali risultati finora ottenuti

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 presented the first sub-exponential algorithm that breaks a long-standing barrier for discounted-sum games with unary weights, and presented algorithms for risk-aware sequential-decision making with risk measures from economics theory. For the second aim for infinite-state stochastic models, we presented automated approaches for quantitative bounds on resource usage of probabilistic programs, and present approaches for analysis of relational properties of probabilistic programs. For the third aim on evolutionary games, we presented a framework to analyse the trade-off between resilience and efficiency of cooperation, and resolved the long-standing open problem of existence of amplifiers in spatial games. Finally, in the fourth aim for applications, we showed the effectiveness of our theoretical methods for analysis of problems arising in reinforcement learning and selfish-mining attacks in blockchains.

Progressi oltre lo stato dell’arte e potenziale impatto previsto (incluso l’impatto socioeconomico e le implicazioni sociali più ampie del progetto fino ad ora)

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, we present new automated approaches for analysis of fundamental problems for probabilistic programs. In the third aim, we present first networks that promotes cooperation in spatial games, resolving a long-standing open problem. All these results are important developments beyond the state of the art. We have demonstrated the practical applicability of our theoretical approaches in AI (e.g. reinforcement learning), and analysis of blockchains. Overall, in all four aims of the project we achieved significant success. By the end of the project, we will finalize the final research questions we are exploring, e.g. extension of the new algorithm to incorporate stochasticity for Aim 1, applying the approaches for security applications for Aim 2, robustness of amplification related to Aim 3. The answers of these questions will finalize the overall results of the project in the next few months.

Stochastic dynamics and emergence of cooperative behavior