Model Checking in multiplayer games development

Multiplayer computer games play a big role in the ever-growing entertainment industry. Being competitive in this industry means releasing the best possible software, and reliability is a key feature to win the market. Computer games are also actively used to simulate different robotic systems where reliability is even more important, and potentially critical. Traditional software testing approaches can check a subset of all the possible program executions, and they can never guarantee complete absence of errors in the source code. On the other hand, during more than twenty years, Model Checking has demonstrated to be a powerful instrument for formal verification of large hardware and software components. In this paper, we contribute with a novel approach to formally verify computer games. We propose a method of model construction that starts from a computer game description and utilizes Model Checking technique. We apply the method on a case study: the game Penguin Clash. Finally, an approach to game model reduction (and its implementation) is introduced in order to address the state explosion problem.

💡 Research Summary

This paper presents a novel methodology for integrating formal verification, specifically Model Checking, into the development process of multiplayer computer games to enhance software reliability. The authors argue that while traditional testing methods are insufficient for guaranteeing the absence of errors across all possible execution paths, Model Checking offers a proven technique for exhaustive verification.

The core contribution is a structured method for constructing a formal model from a game’s natural language description. The game is formally defined as a tuple G = (A, V, V_init, c, OP, EV), comprising a set of Actors (active entities), a set of attribute Vectors (state variables), initial states V_init, constant Parameters (c), an action-assigning function (OP), and an Evolution operator (EV) that defines state transitions based on concurrent actor actions and collision resolutions. This model corresponds to a Nondeterministic Finite Automaton (NFA), which is then translated into a Kripke structure K_G for compatibility with standard model checkers. The proposed workflow involves: 1) building the formal model G from the game design, 2) generating the corresponding Kripke structure, 3) verifying desired properties (e.g., safety and liveness) using a model checker, and 4) translating the verified model into a high-level programming language for integration into the game engine.

To demonstrate the practicality of this approach, the paper details a comprehensive case study using the “Penguin Clash” game, a 2D multiplayer action game featuring penguins that can move, throw snowballs with cooldowns, perform dash attacks, and interact with physics-based collisions. The authors formally define the game’s actors (two penguins, two snowballs), attributes (positions, velocities, states), and evolution rules. Using the NuSMV model checker, they successfully verify several critical properties, such as “a penguin can never have two active snowballs simultaneously” (a safety property enforced by cooldown logic) and “the game eventually terminates if a penguin falls into the water” (a liveness property).

Acknowledging the state explosion problem inherent in model checking complex systems, the paper introduces an approach for game model reduction. This technique involves simplifying the formal model by eliminating details irrelevant to the specific property being verified, thereby making verification computationally feasible. The implementation of this method within a tool called “Safegame” is discussed, which aims to lower the barrier to entry for game developers by automating parts of the model construction and reduction process.

In summary, this work provides a significant step towards bridging the gap between formal verification research and practical game development. It offers a concrete, tool-supported pathway for game designers to mathematically specify and rigorously verify core gameplay mechanics, moving beyond bug detection to providing guarantees about design intent preservation.