2014/04/10 by Avishy Y. Carmi, Carmi, Avishy Y., Daniel Moskovich +1
Computer Science · Engineering · Mathematics · #57M99 #81P68 #94A15 #Advanced Materials and Mechanics #Cellular Automata and Applications #F.0 #FOS: Computer and information sciences #FOS: Electrical engineering #FOS: Mathematics #FOS: Physical sciences #Geometric Topology (math.GT) #Geometric and Algebraic Topology #H.1.1 #Information Theory (cs.IT) #Quantum Physics (quant-ph) #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.1404.2863
openalex publication_date 2014/04/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The preceding paper constructed tangle machines as diagrammatic models, and illustrated their utility with a number of examples. The information content of a tangle machine is contained in characteristic quantities associated to equivalence classes of tangle machines, which are called invariants. This paper constructs invariants of tangle machines. Chief among these are the prime factorizations of a machine, which are essentially unique. This is proven using low dimensional topology, through representing a colour-suppressed machine as a diagram for a network of jointly embedded spheres and intervals in 4-space. The complexity of a tangle machine is defined as its number of prime factors.