In the paper we define three new complexity classes for Turing Machine undecidable problems inspired by the famous Cook/Levin's NP-complete complexity class for intractable problems. These are U-complete (Universal complete), D-complete (Diagonalization complete) and H-complete (Hypercomputation complete) classes. In the paper, in the spirit of Cook/Levin/Karp, we started the population process of these new classes assigning several undecidable problems to them. We justify that some super-Turing models of computation, i.e., models going beyond Turing machines, are tremendously expressive and they allow to accept arbitrary languages over a given alphabet including those undecidable ones. We prove also that one of such super-Turing models of computation - the \$-Calculus, designed as a tool for automatic problem solving and automatic programming, has also such tremendous expressiveness. We investigate also completeness of cost metrics and meta-search algorithms in \$-calculus.

翻译：在本文中，受著名的Cook/Levin NP完全复杂性类（用于描述难解问题）的启发，我们针对图灵机不可判定问题定义了三个新的复杂性类：U-完全（通用完全）类、D-完全（对角化完全）类和H-完全（超计算完全）类。秉承Cook/Levin/Karp的研究思路，我们开始对这些新类进行填充，将多个不可判定问题归入其中。我们论证了某些超图灵计算模型（即超越图灵机的计算模型）具有极其强大的表达能力，能够接受给定字母表上的任意语言，包括那些不可判定的语言。我们还证明，其中一种超图灵计算模型——$\$-演算（一种专为自动问题求解和自动程序设计设计的工具）同样具有这种强大的表达能力。此外，我们研究了$\$-演算中成本度量的完备性以及元搜索算法的完备性。