6 research outputs found
Compositional Modelling of Network Games
The analysis of games played on graph-like structures is of increasing importance due to the prevalence of social networks, both virtual and physical, in our daily life. As well as being relevant in computer science, mathematical analysis and computer simulations of such distributed games are vital methodologies in economics, politics and epidemiology, amongst other fields. Our contribution is to give compositional semantics of a family of such games as a well-behaved mapping, a strict monoidal functor, from a category of open graphs (syntax) to a category of open games (semantics). As well as introducing the theoretical framework, we identify some applications of compositionality
Monoidal Width
We introduce monoidal width as a measure of complexity for morphisms in
monoidal categories. Inspired by well-known structural width measures for
graphs, like tree width and rank width, monoidal width is based on a notion of
syntactic decomposition: a monoidal decomposition of a morphism is an
expression in the language of monoidal categories, where operations are
monoidal products and compositions, that specifies this morphism. Monoidal
width penalises the composition operation along ``big'' objects, while it
encourages the use of monoidal products. We show that, by choosing the correct
categorical algebra for decomposing graphs, we can capture tree width and rank
width. For matrices, monoidal width is related to the rank. These examples
suggest monoidal width as a good measure for structural complexity of processes
modelled as morphisms in monoidal categories.Comment: Extended version of arXiv:2202.07582 and arXiv:2205.0891
Monoidal Width
We introduce monoidal width as a measure of complexity for morphisms in
monoidal categories. Inspired by well-known structural width measures for
graphs, like tree width and rank width, monoidal width is based on a notion of
syntactic decomposition: a monoidal decomposition of a morphism is an
expression in the language of monoidal categories, where operations are
monoidal products and compositions, that specifies this morphism. Monoidal
width penalises the composition operation along ``big'' objects, while it
encourages the use of monoidal products. We show that, by choosing the correct
categorical algebra for decomposing graphs, we can capture tree width and rank
width. For matrices, monoidal width is related to the rank. These examples
suggest monoidal width as a good measure for structural complexity of processes
modelled as morphisms in monoidal categories