Project ART was about Analysing Reduction systems using Transition systems. It was motivated on recent important theoretical developments, in particular:
- the introduction of a new formalism, based on a construction called “(groupoidal) relative pushout” ((G)RPO), within “adhesive” categories. This formalism has allowed the clarification of connections between the large range of different notions of reduction systems, in particular for those notions that use the operational techniques of “double pushout” (DPO).
- the definition of general methodologies that allow one to generate an LTS starting from an RS. This methodology has found a nice integration with the framework of adhesive categories. This project aim to study and clarify the conceptual picture (framework) formed by:
- reduction systems, with particular attention to the ones definable inside adhesive categories;
- labeled transition systems, and their categorical counterpart of coalgebras;
- finally, the methodology of connection between the two approaches, based on the technique of the (G)RPO. This methodology allows one to “synthesize” LTS’s starting from RS’s.
More precisely, this project proceeded in three directions:
- the analysis of the expressivity of the framework, by means of concrete cases studies;
- the further development of the theory of the framework, including comparison with existing approaches, their results and characteristic constructions;
- extensions and modifications of the intial framework, in order to increase expressivity and flexibility.
A lot of nice category theory here, with also lots of applications. At this time I’ve got definitely interested in bigraphs.