普洛金猜想的一个证明

IF 0.4 4区计算机科学 Q4 COMPUTER SCIENCE, SOFTWARE ENGINEERING

Fundamenta Informaticae Pub Date : 2009-06-05 DOI:10.3233/FI-2009-0076

Yinbin Lei, Mao-kang Luo

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引用次数: 1

摘要

1978年G. Plotkin[7]推测，对于三元真值dcpo T，若κ > ω，则函数空间[T$^{κ}$→T$^{κ}$]不是T$^{κ}$的缩回。本文构造性地证明了一个更强的结果，即如果κ > ω，则函数空间[T$^{κ}$→T$^{κ}$]不是任意有限偏集族的笛卡尔积的缩回。由此证明普洛特金猜想是正确的。

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A Proof of Plotkin's Conjecture

In 1978, G. Plotkin [7] conjectured that for the three-element truthvalue dcpo T, if κ > ω then the function space [T$^{κ}$ → T$^{κ}$] is not a retract of T$^{κ}$. In this short paper, we constructively prove a stronger result that if κ > ω then the function space [T$^{κ}$ → T$^{κ}$] is not a retract of the Cartesian product of any family of finite posets. Thus Plotkin's Conjecture is proved to be correct.

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来源期刊

Fundamenta Informaticae 工程技术-计算机：软件工程

CiteScore

2.00

自引率

0.00%

发文量

审稿时长

9.8 months

期刊介绍： Fundamenta Informaticae is an international journal publishing original research results in all areas of theoretical computer science. Papers are encouraged contributing: solutions by mathematical methods of problems emerging in computer science solutions of mathematical problems inspired by computer science. Topics of interest include (but are not restricted to): theory of computing, complexity theory, algorithms and data structures, computational aspects of combinatorics and graph theory, programming language theory, theoretical aspects of programming languages, computer-aided verification, computer science logic, database theory, logic programming, automated deduction, formal languages and automata theory, concurrency and distributed computing, cryptography and security, theoretical issues in artificial intelligence, machine learning, pattern recognition, algorithmic game theory, bioinformatics and computational biology, quantum computing, probabilistic methods, algebraic and categorical methods.