固定参数不可判定的王瓷砖集

AUTOMATA & JAC Pub Date : 2012-08-13 DOI:10.4204/EPTCS.90.6

E. Jeandel, N. Rolin

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引用次数: 5

摘要

如果王牌的数量(或颜色的数量)是有限的，那么决定一组给定的王牌是否允许平面的平铺是可以决定的，因为只有有限的几个这样的平铺集。然而，我们证明，如果瓷砖数量和颜色数量之间的差异以43为界，则瓷砖问题仍然是不可判定的。其中一个主要的新工具是Wang bars的概念，它相当于膨胀的Wang tiles或薄的多骨牌。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Fixed Parameter Undecidability for Wang Tilesets

Deciding if a given set of Wang tiles admits a tiling of the plane is decidable if the number of Wang tiles (or the number of colors) is bounded, for a trivial reason, as there are only finitely many such tilesets. We prove however that the tiling problem remains undecidable if the difference between the number of tiles and the number of colors is bounded by 43. One of the main new tool is the concept of Wang bars, which are equivalently inflated Wang tiles or thin polyominoes.

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