论文信息 - Two-by-Two Substitution Systems and the Undecidability of the Domino Problem

Two-by-Two Substitution Systems and the Undecidability of the Domino Problem

Thanks to a careful study of elementary properties of two-by-two substitution systems, we give a complete self-contained elementary construction of an aperiodic tile set and sketch how to use this tile set to elementary prove the undecidability of the classical Domino Problem.

Nicolas Ollinger

[1] R. Robinson. Undecidability and nonperiodicity for tilings of the plane , 1971 .

[2] Alexander Shen,et al. Fixed Point and Aperiodic Tilings , 2008, Developments in Language Theory.

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

[4] J. Kari. The tiling problem revisited , 2007 .

[5] Robert L. Berger. The undecidability of the domino problem , 1966 .

[6] L. Levin,et al. Local rules and global order, or aperiodic tilings , 2005 .

[7] S. Mozes. Tilings, substitution systems and dynamical systems generated by them , 1989 .

[8] A S Kahr,et al. ENTSCHEIDUNGSPROBLEM REDUCED TO THE AEA CASE. , 1962, Proceedings of the National Academy of Sciences of the United States of America.

[9] Jarkko Kari. The Nilpotency Problem of One-Dimensional Cellular Automata , 1992, SIAM J. Comput..

[10] C. Radin. Miles of tiles , 1999 .

[11] Douglas Lind,et al. An Introduction to Symbolic Dynamics and Coding , 1995 .

[12] Jarkko Kari. The Tiling Problem Revisited (Extended Abstract) , 2007, MCU.