Complejidad prostitutia y computacional en maquinas de Turing pequenas
Complejidad descriptiva y computacional en maquinas de Turing pequenas
摘要：
首先介绍了可计算性理论的基本概念，并介绍了图灵机和计算普适性的概念。然后，我们转向探索不同的复杂性度量之间的权衡，特别是算法（程序大小）和计算（时间）复杂性，作为一种手段来解释这些措施在一个新的方式。调查进行了详尽的探索和系统的研究，由一个大型的小型图灵机与2和3个国家，特别注意运行时，空间使用和模式计算的功能时，机器有机会获得更大的资源（更多的国家）的功能。我们报告说，图灵机计算函数的平均运行时间增加的状态的数量的函数，表明非平凡的机器往往会占用手头的所有资源。一般慢下来，目击和一些偶然的情况下（线性）加速被发现。在我们的研究中遇到各种有趣的结构。我们揭示了在小型图灵机的微观宇宙的结构的研究。
英文摘要：
We start by an introduction to the basic concepts of computability theory and the introduction of the concept of Turing machine and computation universality. Then se turn to the exploration of trade-offs between different measures of complexity, particularly algorithmic (program-size) and computational (time) complexity as a mean to explain these measure in a novel manner. The investigation proceeds by an exhaustive exploration and systematic study of the functions computed by a large set of small Turing machines with 2 and 3 states with particular attention to runtimes, space-usages and patterns corresponding to the computed functions when the machines have access to larger resources (more states). We report that the average runtime of Turing machines computing a function increases as a function of the number of states, indicating that non-trivial machines tend to occupy all the resources at hand. General slow-down was witnessed and some incidental cases of (linear) speed-up were found. Throughout our study various interesting structures were encountered. We unveil a study of structures in the micro-cosmos of small Turing machines.
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