对110规则计算的具体看法
A Concrete View of Rule 110 Computation
摘要：
规则110是执行二进制值的无限行的重复同时更新的元胞自动机。值以以下方式更新：在所有右侧值为1的位置处，0更改为1，而在所有左侧和右侧值均为1的位置处，1更改为0。虽然定义起来很简单，但规则110所展示的行为却令人惊讶地复杂，（Cook，2004）我们证明了它能够通过将图灵机及其磁带编码为重复的左模式、中心模式和重复的右模式来模拟图灵机的活动，在本文中，我们提供了一个显式的编译器转换成规则110的初始状态的图灵机，我们提出了一个一般的方法来证明，这样的结构将工作的预期。模拟最初假设需要指数时间，但Neary和Woods（2006）的惊人结果表明，实际上只需要多项式时间。我们使用Neary和Woods的方法在多项式时间内用标记系统直接模拟图灵机。
英文摘要：
Rule 110 is a cellular automaton that performs repeated simultaneous updates of an infinite row of binary values. The values are updated in the following way: 0s are changed to 1s at all positions where the value to the right is a 1, while 1s are changed to 0s at all positions where the values to the left and right are both 1. Though trivial to define, the behavior exhibited by Rule 110 is surprisingly intricate, and in (Cook, 2004) we showed that it is capable of emulating the activity of a Turing machine by encoding the Turing machine and its tape into a repeating left pattern, a central pattern, and a repeating right pattern, which Rule 110 then acts on. In this paper we provide an explicit compiler for converting a Turing machine into a Rule 110 initial state, and we present a general approach for proving that such constructions will work as intended. The simulation was originally assumed to require exponential time, but surprising results of Neary and Woods (2006) have shown that in fact, only polynomial time is required. We use the methods of Neary and Woods to exhibit a direct simulation of a Turing machine by a tag system in polynomial time.
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