Programme

• Frank Roumen, 13:30 – 14:15

• Matteo Mio, 14:30 – 15:15

• Helle Hvid Hansen, 15:30 – 16:15

Coalgebraic Quantum Computation

Frank Roumen ¹

Various kinds of systems, such as automata and Turing machines, have analogues based on the laws of quantum probability. These can be used as simple theoretical models for quantum computation. We will show how to represent quantum systems as coalgebras, using convex sets of density matrices as state spaces. The general theory of minimization for coalgebras will provide a method to convert quantum mechanical systems into simpler probabilistic systems with the same behaviour.

A note on Convex Bisimilarity (Work in Progress)

Matteo Mio ²

In this talk I will describe my current research on the semantics of probabilistic nondeterministic systems (aka, Simple Segala systems). It has been argued by several authors that ordinary bisimilarity is too strict as a notion of behavioral equivalence for processes. I will argue in favor of the coarser “convex” bisimilarity on the basis of well-known arguments (such as, e.g., probabilistic schedulers) and possibly new ones.

Distributive laws for monads with equations

Helle Hvid Hansen ^{1 2}

Behavioural differential equations and abstract GSOS are well known methods for specifying structured behaviour. Technically, this amounts to giving a distributive law of a free monad over a behaviour functor. However, for several applications, e.g. context-free grammars, the monad in question is not free, and it can be rather difficult to describe a distributive law explicitly. We show how to obtain a distributive law for a monad with an equational presentation from a distributive law for the underlying free monad that preserves the equations.