5 papers · 1 filter
Two-Dimensional Billiards Are Turing Complete
Eva Miranda, Isaac Ramos
We show that two-dimensional billiard systems can simulate universal Turing machines. Billiards serve as idealized models of particle motion with elastic reflections and arise natu…
Topological entropy of Turing complete dynamics
Renzo Bruera, Robert Cardona, Eva Miranda +2
We explore the relationship between Turing completeness and topological entropy of dynamical systems. We first prove that a natural class of Turing machines that we call "branching…
Topological Kleene Field Theories as a model of computation
Ãngel González-Prieto, Eva Miranda, Daniel Peralta-Salas
In this article, we establish the foundations of a computational field theory, which we term Topological Kleene Field Theory (TKFT), inspired by Stephen Kleene's seminal work on pa…
Universality in computable dynamical systems: Old and new
Ãngel González-Prieto, Eva Miranda, Daniel Peralta-Salas
The relationship between computational models and dynamics has captivated mathematicians and computer scientists since the earliest conceptualizations of computation. Recently, thi…
Towards a Fluid computer
Robert Cardona, Eva Miranda, Daniel Peralta-Salas
In 1991, Moore [20] raised a question about whether hydrodynamics is capable of performing computations. Similarly, in 2016, Tao [25] asked whether a mechanical system, including a…