ChatGPT:

To handle the complexities and nuances inherent in computer systems, various models and formalisms have been developed. Here are a few examples:

Turing machines: Turing machines are theoretical models of computation that allow for the representation of complex algorithms and computations. They can handle infinite tape storage, non-determinism, and unbounded computation, providing a more expressive representation than FSAs

Turing machines are imaginary systems characterized by an infinite tape that later ChatGPT admits that such a tape cannot exist. It is, therefore, a contradiction to reject my proposal that it does not apply to an imaginary kind of machine.

Petri nets: Petri nets are graphical models used to represent concurrent and distributed systems. They can capture the concurrency and synchronization of processes, the flow of resources, and the interactions between components, making them suitable for modeling complex systems with parallelism and synchronization requirements.

It is very easy to describe any set of parallel processes as an FSA whose state consists of the combination of the states of each constituent process.

Process calculi: Process calculi, such as the π-calculus or the communicating sequential processes (CSP) model, are formal frameworks for describing concurrent systems. They provide formal notations and rules to represent processes, communication, and synchronization between concurrent components, allowing for precise modeling and analysis of concurrent behavior

State charts: State charts are an extension of FSAs that incorporate hierarchical states, concurrent states, and events. They provide a more expressive way to model complex systems with multiple levels of abstraction and parallel behavior. State charts are widely used in software engineering and graphical modeling languages such as UML.

Formal methods: Formal methods encompass a range of mathematical techniques, such as model checking, theorem proving, and abstract interpretation, to analyze and verify properties of computer systems. These methods use formal logic and mathematical reasoning to reason about system behavior, correctness, safety, and security.

Agent-based models: Agent-based models represent systems as a collection of autonomous and interacting agents. Each agent has its own behavior, state, and communication capabilities. These models are used to simulate and analyze complex systems involving multiple entities and their interactions.

These models and formalisms, among others, provide more advanced representations for handling the complexities and nuances of computer systems. They offer greater expressive power and analytical capabilities beyond what can be captured by simple FSAs, allowing for a deeper understanding and analysis of complex system behaviors.
