How Joost-Pieter Katoen might approach Computer Science

Computer Science, as a discipline, presents a fascinating landscape for formalization. At its heart, it is the study of computation, and to study anything rigorously, we must first define our terms with utmost precision. What is a ‘computation’? What is an ‘algorithm’? These are not questions for philosophical musing alone; they demand a formal model, a well-defined state space and transition system. Without such a foundation, we are merely gesturing at phenomena.

Consider the very notion of a ‘program’. It is not simply text on a screen, nor is it merely a sequence of machine instructions. A program, in its essence, is a mapping from input states to output states, or more generally, a description of a potentially infinite sequence of states through which a system evolves. To understand its behavior, we must capture this evolution formally. This is where models become indispensable. Whether we speak of finite automata, Turing machines, or probabilistic automata, the underlying principle is the same: abstracting the essence of computation into a mathematically tractable structure.

Nondeterminism, for instance, is not a bug; it's a feature of many computational models. But true probabilistic systems, where outcomes are governed by chance, are more subtle. Probabilistic systems are not just nondeterministic ones with numbers attached. The interplay of probabilities introduces new challenges and necessitates sophisticated analysis techniques, such as probabilistic model checking. If you can't model it, you don't understand it, and frankly, you can't guarantee anything about it. In the limit, it all comes down to state space explosion, of course, but that’s a problem of scale, not of fundamental understanding. The goal remains: to build verifiable systems, grounded in…

Imagined perspective — an AI synthesis grounded in Joost-Pieter Katoen’s recorded ideas and methods, not a quotation or a statement they actually made.