主 题: Concrete coalgebra: a mini course
报告人: Prof. Jan Rutten (CWI
时 间: 2012-05-14, 15 ,16 15:00-17:00
地 点: 理科一号楼 1418
Coalgebra is a unifying framework for studying the behaviour of state-based systems,
many of which are of fundamental interest in computer science. Examples include all
kinds of infinite data types, such as streams (that is, infinite sequences) and trees.
Other examples are deterministic and nondeterministic automata, labelled and probabilistic
transition systems, etc.
Coalgebra is a rather recent field of research, existing for mere two decades, and it is
attracting an enthusiastic, ever-growing community. Being relatively young, it still has many
elementary and exciting research questions to offer.
The general theory of universal coalgebra provides general notions of observable behaviour
and bisimilarity, as well as a powerful and fascinating reasoning principle called coinduction
(a notion that is dual to the well known induction principle).
In these lectures, we will start by studying how basic examples of datatypes, such as infinite
streams and trees, can be modeled as coalgebras. Next, we will show how fundamental notions
and constructions, such as language equivalence of automata and determinisation of nondeterministic
automata, are instances of more general concepts from coalgebra.
Here is a (tentative) table of contents of the lectures:
1. The coalgebraic perspective on the behaviour of systems
2. Streams and coinduction
3. Streams and circuits
4. Automata (I)
5. Automata (II)
6. Advanced topics in coalgebra