Tiling problems, automata, and tiling graphs
نویسندگان
چکیده
منابع مشابه
Tiling Problems
The undecidable problems we saw at the start of our unit on undecidability were all questions about the behavior of computer programs. But in fact there are many decision problems which, on the surface, have nothing to do with computer programs yet can still be proved to have no algorithmic solution. One of these is a tiling problem. Imagine square tiles divided into colored triangular quadrants.
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We define a convolution operation on the set of polyominoes and use it to obtain a criterion for a given polyomino not to tile the plane (rotations and translations allowed). We apply the criterion to several families of polyominoes, and show that the criterion detects some cases that are not detectable by generalized coloring arguments.
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Fallenstein and Soares [2014] demonstrates that it’s possible for certain types of proof-based agents to “tile” (license the construction of successor agents similar to themselves while avoiding Gödelian diagonalization issues) in environments about which the agent can prove some basic nice properties. In this technical report, we show via a similar proof that causal graphs (with a specific str...
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متن کاملTiling Problems A.1 Introduction
In this appendix, we prove the undecidability of the following problems: the constrained domino problem (proved undecidable by Wang): give a tile set and a tile as input, ask whether it is possible to form a tiling of the plane containing the given tile; the unconstrained domino problem (Berger's Theorem): the input is a tile set and the question is whether one can tile the plane with it; the p...
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ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 2008
ISSN: 0304-3975
DOI: 10.1016/j.tcs.2008.07.019