Universality and Cellular Automata

The classification of discrete dynamical systems that are computationally complete has recently drawn attention in light of Wolfram's "Principle of Computational Equivalence". We discuss a classification for cellular automata that is based on computably enumerable degrees. In this setting the full structure of the semilattice of the c.e. degrees is inherited by the cellular automata. 1 Intermediate Degrees and Computational Equivalence One of the celebrated results of recursion theory in the 20th century is the positive solution to Post's problem: there are computably enumerable sets whose Turing degree lies strictly between , the degree of any recursive set, and , the degree of the Halting set or any other complete computably enumerable set. The result was obtained independently and almost simultaneously by R. M. Friedberg and A. A. Muchnik, see [8, 14]. The method used in their construction of an intermediate degree is remarkable since it departs significantly fr...

• Type: Conference
• Year: 2004
• Where: MCU
• Authors: Klaus Sutner
• Keywords: Cellular Automata, Enumerable Degree, Enumerable Set, MCU 2004, MCU 2007