论文标题
整数上的可同步功能
Synchronizable functions on integers
论文作者
论文摘要
对于所有自然数a，b和d> 0，我们考虑函数f_ {a，b，d}，该函数将n/d连接到任何整数n时，当它为d的倍数时，否则将其连接到a + b。特别是f_ {3,1,2}是collatz函数。用b <a在基础a> 1中编码，我们通过输入确定的字母到字母传感器，并带有其他输出最终单词来意识到这些功能。该特定形式允许在任何整数n中阐明这种传感器的组成n时间，以计算f^n_ {a，b，d}。我们甚至通过无限输入 - 确定的字母对字母传感器的构图下的封闭f^*_ {a，b，d，具有常规的初始状态和长度循环终端函数。
For all natural numbers a,b and d > 0, we consider the function f_{a,b,d} which associates n/d to any integer n when it is a multiple of d, and an + b otherwise; in particular f_{3,1,2} is the Collatz function. Coding in base a > 1 with b < a, we realize these functions by input-deterministic letter-to-letter transducers with additional output final words. This particular form allows to explicit, for any integer n, the composition n times of such a transducer to compute f^n_{a,b,d}. We even realize the closure under composition f^*_{a,b,d by an infinite input-deterministic letter-to-letter transducer with a regular set of initial states and a length recurrent terminal function.
