小型图灵机的程序大小与时间复杂度、加速与减速现象
Program-Size Versus Time Complexity, Speed-Up and Slowdown Phenomena in Small Turing Machines
摘要：
本文的目的是进行一个实验研究之间的权衡程序大小和时间计算复杂性。调查包括一个详尽的探索和系统的研究的功能计算的所有2色图灵机与2，3和4个状态-表示为（n，2）与n的状态数-特别注意的运行时间和空间使用时，机器可以访问更大的资源（更多的状态）。我们报告说，图灵机计算函数的平均运行时间几乎肯定会随着状态数的增加而增加，这表明没有立即终止的机器往往会占用手头的所有资源。我们计算了所有的时间复杂度类的算法计算的函数（2，2）和（3，2）属于，并在这些类之间进行了比较。对于选择的函数，比较扩展到（4，2）。我们的研究揭示了小型图灵机微观世界的各种结构。最值得注意的是，我们观察到的“相变”的停顿概率分布，我们解释。此外，可以观察到，短的初始段完全定义了由图灵机计算的函数。
英文摘要：
The aim of this paper is to undertake an experimental investigation of the trade-offs between program-size and time computational complexity. The investigation includes an exhaustive exploration and systematic study of the functions computed by the set of all 2-color Turing machines with 2, 3 and 4 states--denoted by (n,2) with n the number of states--with particular attention to the runtimes and space usages when the machines have access to larger resources (more states). We report that the average runtime of Turing machines computing a function almost surely increases as a function of the number of states, indicating that machines not terminating (almost) immediately tend to occupy all the resources at hand. We calculated all time complexity classes to which the algorithms computing the functions found in both (2,2) and (3,2) belong to, and made a comparison among these classes. For a selection of functions the comparison was extended to (4,2). Our study revealed various structures in the micro-cosmos of small Turing machines. Most notably we observed "phase-transitions" in the halting-probability distribution that we explain. Moreover, it is observed that short initial segments fully define a function computed by a Turing machine.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
