A formal approach to spatio-temporal modeling of game systems

This article introduces FAST-GM (Formal Approach to Spatio-Temporal Game Modeling), a new unified approach to formal modeling of game entities and their interactions that integrates temporal and probabilistic dimensions, thus offering a comprehensive framework for capturing the dynamics of game systems. Built upon the principles of extended temporal logic and probability theory, FAST-GM accurately describes complex game mechanics and how they evolve. A formal definition of game entities was considered. Their states and interactions were explored. The methods for integrating temporal and probabilistic elements into gameplay were discussed. The applicability of FAST-GM for game balancing, formal verification of game scenarios, and automated generation of test cases was analyzed. Its scalability and adaptability in various game genres were assessed. The results obtained show that FAST-GM should advance the formal modeling of game systems, equipping developers with a powerful toolset for analysis, verification, and optimization of game mechanics throughout the process of creating a video game.