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On 1 July 2014, Joost Winter defended his thesis on connections between coalgebra and automata theory. Coalgabra is an abstract framework for the description of and formal reasoning about multi-state systems. One of the uses is to prove that systems meet certain requirements, such as the correctness of a complex software system.
In his thesis, Winter applies coalgebraic principles in automata theory, a theoretical framework for describing automata. Winter describes known classes in automata theory such as regular and context-free grammars (and its generalizations) in the form of (discrete) differential equations. This clarifies the connections between classical automata theory, developed since the 50’s and 60’s, and the modern coalgebraic approach.
Centrum Wiskunde & Informatica (CWI) is considered the birthplaceof universal coalgebra. Prof. dr. Jan Rutten introduced this field in a paper in 2000. Currently, this paper has been cited more than a 1,000 times, and several research groups worldwide are working on this topic.
Image: A Turing machine is an example of an automaton that can be described with automata theory. A Turing machine is a model for computation developed by Alan Turing in 1937, and stood at the basis of the modern computer. The image shows a Turing machine created with LEGO Mindstorms by CWI researchers in 2012. www.legoturingmachine.org