Early work by von Neumann focused on selfreproducing structures and universal construction in cellular automata, although many of the proposed CAs were also computationally universal. INTRODUCTION Computation with cellular automata (CA) has an interesting history. Categories and Subject Descriptors F.1.1 : Models of Computation-cellular automata Keywords Cellular automata universality models of computation 1. We prove in this paper that a tight bound on its size. This automaton is directly inspired by the factor matrix defined by Conway thirty years ago. We give the first known example of a physically universal CA, answering an open problem of Janzing and opening the way for further research in this area. The universal automaton of a regular language is the maximal NFA without merging states that recognizes this language. A cellular automaton is physically universal if it is possible to implement any transformation on a finite region of the CA by initializing the complement of the region and letting the system evolve. In this paper, we consider a different kind of universality proposed by Janzing. Cambridge, MA 02139 ABSTRACT Several cellular automata (CA) are known to be universal in the sense that one can simulate arbitrary computations (e.g., circuits or Turing machines) by carefully encoding the computational device and its input into the cells of the CA. In 1982, Berlekamp, Conway and Guy showed that Conway's GameĪ Physically Universal Cellular Automaton Luke Schaeffer Massachusetts Institute of Technology 77 Massachusetts Ave. We give the first known example of a physically universal CA, answering an open problem of Janzing and opening the way for further research in this area. A Physically Universal Cellular Automaton A Physically Universal Cellular AutomatonĪ Physically Universal Cellular Automaton Luke Schaeffer Massachusetts Institute of Technology 77 Massachusetts Ave.
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