A universal cellular automaton in the hyperbolic plane

Theoretical Computer Science

Volumn 296, Issue 2, 2003, Pages 327-364

  Herrmann, Francine ^a   Margenstern, Maurice ^a  

^a UNIVERSITÉ DE LORRAINE   (France)

Author keywords

Cellular automata; Circuits; Hyperbolic plane; Registers; Switches; Universality

Indexed keywords

ALGORITHMS; GRAPH THEORY; LOGIC CIRCUITS; PARALLEL PROCESSING SYSTEMS; POLYNOMIALS;

CELLULAR AUTOMATION;

TURING MACHINES;

EID: 0037426286     PISSN: 03043975     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0304-3975(02)00660-6     Document Type: Conference Paper

References (17)

1. Carathéodory C. Theory of Functions of a Complex Variable. Vol. II:1954;177-184 Chelsea, New York.
2. M. Delorme, J. Mazoyer (Eds.), Cellular Automata, a Parallel Model, Vol. 460, Kluwer Academic Publishers, Dordrecht, 1999, 373pp.
3. J. Gruska, Foundations of Computing, International Thomson Computer Press, Boston, USA, 1997, 716pp.
4. F. Herrmann, M. Margenstern, K. Morita, Cellular automata in the hyperbolic plane: implementing a polynomial algorithm to solve SAT problem, CA2000, Osaka (Japan), August 21-22, 2000, pp. 25-26.
5. Ch. Iwamoto, M. Margenstern, K. Morita, T. Worsch, P=NP in the space of cellular automata of the hyperbolic plane, AUTOMATA 2001, Porqueyrolles, France, September 27-29, 2001.
6. M. Margenstern, Cellular automata in the hyperbolic plane, Technical Report, Publications du GIFM, I.U.T. of Metz, No. 99-103, 1999, 34p, ISBN 2-9511539-3-7.
7. Margenstern M. New tools for cellular automata in the hyperbolic plane. J. Universal Comput. Sci. 6(12):2000;1226-1252.
8. Margenstern M. Two railway circuits. a universal circuit and an NP-difficult one Comput. Sci. J. Moldova. 9(1):2001;3-33.
9. Margenstern M., Morita K. NP problems are tractable in the space of cellular automata in the hyperbolic plane. Theoret. Comput. Sci. 259:2001;99-128.
10. Minsky M.L. Computation. Finite and Infinite Machines:1967;Prentice-Hall, Englewood Cliffs, NJ.
11. Morgenstein D., Kreinovich V. Which algorithms are feasible and which are not depends on the geometry of space-time. Geombinatorics. 4:1995;80-97.
12. K. Morita, A simple construction method of a reversible finite automaton out of Fredkin gates, and its related problem, Trans. IEICE Japan, E73 (1990) 978-984.
13. Poincaré H. Théorie des groupes fuchsiens. Acta Math. 1:1882;1-62.
14. A. Ramsay, R.D. Richtmyer, Introduction to Hyperbolic Geometry, Springer, Berlin, 1995, 287pp.
15. Robinson R.M. Undecidable tiling problems in the hyperbolic plane. Invent. Math. 44:1978;259-264.
16. Róka Zs. One-way cellular automata on Cayley Graphs. Theoret. Comput. Sci. 132:1994;259-290.
17. I. Stewart, A Subway Namet Turing, Mathematical Recreations in Scientific American 1994, 90-92.