Determining a regular language by glider-based structures called phases fi_1 in Rule 110

Rule 110 is a complex elementary cellular automaton able of supporting universal computation and complicated collision-based reactions between gliders. We propose a representation for coding initial conditions by means of a finite subset of regular expressions. The sequences are extracted both from de Bruijn diagrams and tiles specifying a set of phases fi_1 for each glider in Rule 110. The subset of regular expressions is explained in detail.

[1]  Martin D. Davis,et al.  Computability and Unsolvability , 1959, McGraw-Hill Series in Information Processing and Computers.

[2]  A. Turing.  On Computable Numbers, with an Application to the Entscheidungsproblem. , 1937 .

[3]  G. C. Shephard,et al.  Tilings and Patterns , 1990 .

[4]  Matthew Cook,et al.  Universality in Elementary Cellular Automata , 2004, Complex Syst..

[5]  Stephen Wolfram.  One-dimensional Cellular Automata , .

[6]  Mats G. Nordahl,et al.  Formal Languages and Finite Cellular Automata , 1989, Complex Syst..

[7]  Genaro J. Martínez.  Introduction to OSXLCAU21 System , 2004 .

[8]  Jeffrey D. Ullman,et al.  Introduction to Automata Theory, Languages and Computation , 1979 .

[9]  Stephen Wolfram,et al.  A New Kind of Science , 2003, Artificial Life.

[10]  Michael A. Arbib,et al.  Theories of abstract automata , 1969, Prentice-Hall series in automatic computation.

[11]  James P. Crutchfield,et al.  Quantum automata and quantum grammars , 2000, Theor. Comput. Sci..

[12]  Jarkko Kari,et al.  New Results on Alternating and Non-deterministic Two-Dimensional Finite-State Automata , 2001, STACS.

[13]  Turlough Neary,et al.  P-completeness of Cellular Automaton Rule 110 , 2006, ICALP.

[14]  守屋 悦朗,et al.  J.E.Hopcroft, J.D. Ullman 著, "Introduction to Automata Theory, Languages, and Computation", Addison-Wesley, A5変形版, X+418, \6,670, 1979 , 1980 .

[15]  H. Stone.  Discrete Mathematical Structures and Their Applications , 1973 .

[16]  Andrew Adamatzky,et al.  Computing in nonlinear media and automata collectives , 2001 .

[17]  Harold V. McIntosh,et al.  ATLAS: Collisions of gliders as phases of ether in rule 110 , 2001 .

[18]  J. Kurths,et al.  Complexity of two-dimensional patterns , 2000 .

[19]  B. Voorhees.  Computational Analysis of One-Dimensional Cellular Automata , 1995 .

[20]  Michael A Arbib,et al.  Theories of abstract automata (Prentice-Hall series in automatic computation) , 1969 .

[21]  Juan Carlos Seck Tuoh Mora,et al.  Rule 110 Objects and Other Collision-Based Constructions , 2007, J. Cell. Autom..

[22]  Edward F. Moore,et al.  Gedanken-Experiments on Sequential Machines , 1956 .

[23]  Lyman P. Hurd.  Formal Language Characterization of Cellular Automaton Limit Sets , 1987, Complex Syst..

[24]  Klaus Sutner,et al.  Computation theory of cellular automata , 1998 .

[25]  Juan Carlos Seck Tuoh Mora,et al.  Production of Gliders by Collisions in Rule 110 , 2003, ECAL.

[26]  Stephen Wolfram,et al.  Theory and Applications of Cellular Automata , 1986 .

[27]  A. Church.  Edward F. Moore. Gedanken-experiments on sequential machines. Automata studies , edited by C. E. Shannon and J. McCarthy, Annals of Mathematics studies no. 34, litho-printed, Princeton University Press, Princeton1956, pp. 129–153. , 1958, Journal of Symbolic Logic.

[28]  Kenichi Morita,et al.  Simple Universal One-Dimensional Reversible Cellular Automata , 2007, J. Cell. Autom..

[29]  K. Steiglitz,et al.  Soliton-like behavior in automata , 1986 .

[30]  Burton Voorhees.  Remarks on Applications of De Bruijn Diagrams and Their Fragments , 2008, J. Cell. Autom..

[31]  Juan Carlos Seck Tuoh Mora,et al.  Gliders in Rule 110 , 2006, Int. J. Unconv. Comput..