2017/02/18 by Diego Maldonado, Anahí Gajardo, Maldonado, Diego +5 · 1 citation
Computer Science · #68Q05 #68Q17 #Algorithms and Data Compression #Cellular Automata and Applications #Cellular Automata and Lattice Gases (nlin.CG) #Computability, Logic, AI Algorithms #Computational Complexity (cs.CC) #F.1.1 #F.1.3 #FOS: Computer and information sciences #FOS: Physical sciences
paper · pdf · doi:10.48550/arxiv.1702.05547
openalex publication_date 2017/02/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A Turmit is a Turing machine that works over a two-dimensional grid, that is, an agent that moves, reads and writes symbols over the cells of the grid. Its state is an arrow and, depending on the symbol that it reads, it turns to the left or to the right, switching the symbol at the same time. Several symbols are admitted, and the rule is specified by the turning sense that the machine has over each symbol. Turmites are a generalization of Langtons ant, and they present very complex and diverse behaviors. We prove that any Turmite, except for those whose rule does not depend on the symbol, can simulate any Turing Machine. We also prove the P-completeness of prediction their future behavior by explicitly giving a log-space reduction from the Topological Circuit Value Problem. A similar result was already established for Langtons ant; here we use a similar technique but prove a stronger notion of simulation, and for a more general family.