费用函数的计算

摘要：

费用函数提供了一个框架，用于构造接近可计算的停机问题下的图灵集。我们对费用函数进行了系统的研究。我们将它们的代数性质与它们的表达能力联系起来。我们证明了加性费用函数类描述了$K$ -平凡集。我们证明了一个费用函数的基础定理，并给出了一个一般的建设可计算的可计算集，接近图灵完备。该作品可追溯到2010年，并于2013年提交给2012年剑桥图灵年产生的长期延迟卷“The Incomputable”。

英文摘要：

Cost functions provide a framework for constructions of sets Turing below the halting problem that are close to computable. We carry out a systematic study of cost functions. We relate their algebraic properties to their expressive strength. We show that the class of additive cost functions describes the $K$-trivial sets. We prove a cost function basis theorem, and give a general construction for building computably enumerable sets that are close to being Turing complete. This works dates from 2010 and was submitted in 2013 to the long-delayed volume "The Incomputable" arising from the 2012 Cambridge Turing year.

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。