Jarosław Miller
supervisor: Agata Pilitowska
The use of category theory as an abstract description language used in theoretical computer science has gained great popularity in the last two decades because it allows for the unification of seemingly independent fields of computer science. The main goal of my research work is to present new theory-categorical models of concurrent computation that can be placed in the context of other aspects of computation, such as computation with indiscreet time or probabilistic computation. Research focuses on presenting abstract, general extensions of pi-calculus and their semantics.
The pi-calculus is the language of description of processes operating in parallel and communicating with each other. Research on it is one of the core of the development of the field of formal methods and often finds practical applications, e.g. in proving the correctness of cryptographic algorithms. In theoretical and practical considerations on the pi-calculus, its extensions are often introduced, departing from its classical form. In many cases, this requires building a theory from scratch: introducing a new language and its semantics (somewhat different from the classical one), and then proving the correctness of the defined structures. Despite some advantages of this approach, it is not a modular approach. The modular approach is to build a general abstract theory in which new constructs and results would be instances of it.