{"title":"A Proof of Plotkin's Conjecture","authors":"Yinbin Lei, Mao-kang Luo","doi":"10.3233/FI-2009-0076","DOIUrl":null,"url":null,"abstract":"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.","PeriodicalId":56310,"journal":{"name":"Fundamenta Informaticae","volume":null,"pages":null},"PeriodicalIF":0.4000,"publicationDate":"2009-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.3233/FI-2009-0076","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Fundamenta Informaticae","FirstCategoryId":"94","ListUrlMain":"https://doi.org/10.3233/FI-2009-0076","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"COMPUTER SCIENCE, SOFTWARE ENGINEERING","Score":null,"Total":0}
引用次数: 1
Abstract
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.
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.
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