Traditional computability theory does not fully capture the essence of computation. It focuses on what can be computed, neglecting how things are computed. I will present a mathematization of computer science fundamental notions, grounded in the theory of dynamical systems, which prioritizes the ‘how’ over the ‘what’. This approach has numerous implications, enabling:
- A uniform account of existing lower bounds, and new lower bound results, in algebraic complexity
- Static analysis methods which can be implemented in usable tools
- The definition of new dynamical models of linear logic
- New perspectives on implicit computational complexity and the formal definition of the notion of algorithm
In this talk, I will focus on two applications:
- discretizing abstract programs for static analysis (related to 2. and 4.)
- extracting mathematical structure from corpora to understand large language models (related to 3. and 4.)
