一类NP完全问题的无限解
Infinite versions of some NP-complete problems
摘要：
最近，图论中有限问题的复杂性和无限问题的复杂性之间的联系已经被探索。正如我们的论文（以及Tirza Hirst和D. Harel从不同的角度），这些复杂性之间没有牢固的联系，即相同复杂性的有限问题对于无限版本可能具有根本不同的复杂性，反之亦然。此外，无限对应物的复杂性在很大程度上取决于有限问题在无限情况下如何重新表述。我们解决的有限问题包括图的可着色性和子图同构的存在性。特别是，我们给出了三个无限版本的3-着色性问题，其递归理论和证明理论的复杂性有很大的不同。此外，我们表明，不同的有限复杂度的三个子图同构问题具有相同的递归理论和证明理论的内容的无限版本。
英文摘要：
Recently, connections have been explored between the complexity of finite problems in graph theory and the complexity of their infinite counterparts. As is shown in our paper (and in independent work of Tirza Hirst and D. Harel from a different angle) there is no firm connection between these complexities, namely finite problems of equal complexity can have radically different complexity for the infinite versions and vice versa. Furthermore, the complexity of an infinite counterpart can depend heavily on precisely how the finite problem is rephrased in the infinite case. The finite problems we address include colorability of graphs and existence of subgraph isomorphisms. In particular, we give three infinite versions of the 3-colorability problem that vary considerably in their recursion theoretic and proof theoretic complexity. Additionally, we show that three subgraph isomorphism problems of varying finite complexity have infinite versions with identical recursion theoretic and proof theoretic content.
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。
