My name is Musashi Koyama. I am a student at Monash University studying science. I am interested in Mathematics, particularly vector calculus.
Programming with Topology
Outline: A finite state machine, or finite state automation, is an abstract mathematical model of computation. Without any memory, finite state machines are simpler than Turing machines, but can still perform many important tasks and have important applications in computer science, engineering and linguistics.The simplicity of finite state machines raises the interesting possibility that they can be modelled by mathematical structures ostensibly far removed from computer science. In particular, recent work in contact geometry, a branch of mathematics related to classical mechanics, optics and thermodynamics has raised the possibility of representing finite state machines by simply considering the topology of curves on surfaces.This project will study methods of representing finite state machines, and investigate whether they can be implemented by constructions as simple as drawing curves on surfaces: ‘programming with topology’.