Causality, Time flow and Abstraction in Networks

• Applicant: Mathilde Noual, Ph.D.
• Subject Area: Theoretical Computer Science
• Term: from 2017 to 2021
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 335775530

Boolean Automata Networks (BANs) are formal prototypes of 'networks', a.k.a. 'interaction system'. They not only can serve as (simplistic) models of real networks. They also capture the core of what a network is. My project uses them as such to study 'networkness'. It focuses on general, notable, scalable BAN features (e.g. synchronism, reversibility, non-monotony), and addresses questions about (i) the intrinsic effect of these features, (ii) their vicariousness, i.e. the different ways to formally implement the effects that they are known, recognised and sometimes disregarded for, (iii) their expressivity and the consistency of their possible meanings with respect to the meanings of other pre-existing meaningful features of the formalism. The primary overarching aims of the project are (1) to help build a portable, thorough and constructive understanding of networkness, (2) develop foundations of a theory of time flow in networks, and (3) provide formal, transdisciplinarily practical grips on the notion of 'abstraction' attendant to network representation and observation. In the longer term, the project is expected to (a) help organise and pool the literature's pre-existing results on Automata Networks, (b) promote transdisciplinary dialogue, and (c) emphasise the urgent, pivotal role that Fundamental Computer Science may play right at the centre of the 'applied' nature-modelling sciences. To make progress in those directions, I propose to apply discrete mathematical tools, and define a strict methodological guideline based on the intuitive notion of causality.

• DFG Programme: Research Grants