通过结构转换的隐式复杂性
Implicit complexity via structure transformation
摘要：
隐式计算复杂性，其目的是通过机器无关的手段来表征复杂性类，传统上一方面基于自由代数的程序和演绎形式主义，另一方面基于有限结构的描述工具。我们在这里考虑“未解释”的程序的有限结构的转换，它定义的功能，在一个自由代数A一旦元素的A本身被认为是有限的结构。因此，我们弥合了上述两种方法之间的差距隐式复杂性，精简和澄清重要的工具和技术，如集存在和分歧的潜力。我们说明了这种潜力，描绘了一个广泛的类的程序，循环变体熟悉的概念的基础上，从强制性的程序建设，其特点是一个通用的概念，连续递归的复杂性，没有参考任何数据驱动的复发。
英文摘要：
Implicit computational complexity, which aims at characterizing complexity classes by machine-independent means, has traditionally been based, on the one hand, on programs and deductive formalisms for free algebras, and on the other hand on descriptive tools for finite structures. We consider here "uninterpreted" programs for the transformation of finite structures, which define functions over a free algebra A once the elements of A are themselves considered as finite structures. We thus bridge the gap between the two approaches above to implicit complexity, with the potential of streamlining and clarifying important tools and techniques, such as set-existence and ramification. We illustrate this potential by delineating a broad class of programs, based on the notion of loop variant familiar from imperative program construction, that characterizes a generic notion of primitive-recursive complexity, without reference to any data-driven recurrence.
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。
