点灯程序的生成与分析
Generation and analysis of lamplighter programs
摘要：
我们考虑一个程序设计语言的基础上，只使用组合和迭代作为控制结构的lampighter组。我们推导出生成函数和计数公式，这种语言和它的特殊子集，建立语义不同的程序的增长率上下限。最后，我们展示了如何对随机程序进行采样，并分析了由这种采样引起的运行时分布。
英文摘要：
We consider a programming language based on the lamplighter group that uses only composition and iteration as control structures. We derive generating functions and counting formulas for this language and special subsets of it, establishing lower and upper bounds on the growth rate of semantically distinct programs. Finally, we show how to sample random programs and analyze the distribution of runtimes induced by such sampling.
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。
