The periodic domino problem revisited

In this article, we give a new proof of the undecidability of the periodic domino problem. Compared to previous proofs, the main difference is that this one does not start from a proof of the undecidability of the (general) domino problem but only from the existence of an aperiodic tileset.

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

[2]  Stål Aanderaa,et al.  Linear Sampling and the forall exists forall Case of the Decision Problem , 1974, J. Symb. Log..

[3]  Hao Wang Proving theorems by pattern recognition — II , 1961 .

[4]  Philip K. Hooper The undecidability of the Turing machine immortality problem , 1966, Journal of Symbolic Logic.

[5]  Alexander Shen,et al.  Fixed-point tile sets and their applications , 2009, J. Comput. Syst. Sci..

[6]  Hao Wang Notes on a class of tiling problems , 1975 .

[7]  Karel Culík,et al.  An aperiodic set of 13 Wang tiles , 1996, Discret. Math..

[8]  Pascal Vanier,et al.  Periodicity in tilings , 2009, Developments in Language Theory.

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

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

[11]  Gabor T. Herman Review: Philip K. Hooper, The Undecidability of the Turing Machine Immortality Problem , 1971 .

[12]  Yuri Gurevich,et al.  The Classical Decision Problem , 1997, Perspectives in Mathematical Logic.

[13]  Jarkko Kari,et al.  Periodicity and Immortality in Reversible Computing , 2008, MFCS.

[14]  Nicolas Ollinger Two-by-Two Substitution Systems and the Undecidability of the Domino Problem , 2008, CiE.

[15]  Jarkko Kari,et al.  A small aperiodic set of Wang tiles , 1996, Discret. Math..

[16]  Branko Grünbaum,et al.  Aperiodic tiles , 1992, Discret. Comput. Geom..

[17]  Vincent D. Blondel,et al.  On the presence of periodic configurations in Turing machines and in counter machines , 2002, Theoretical Computer Science.

[18]  Jirí Matousek,et al.  Efficient partition trees , 1991, SCG '91.

[19]  Y. Gurevich,et al.  Remarks on Berger's paper on the domino problem , 1972 .

[20]  Harry R. Lewis,et al.  Unsolvable classes of quantificational formulas , 1979 .

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