{"title":"Growth and irreducibility in path-incompressible trees","authors":"George Barmpalias, Xiaoyan Zhang","doi":"10.1016/j.ic.2024.105136","DOIUrl":null,"url":null,"abstract":"<div><p>We study randomness-preserving transformations of path-incompressible trees, namely trees of finite randomness deficiency. We characterize their branching density, and show: (a) sparse perfect path-incompressible trees can be effectively densified, almost surely; (b) there exists a path-incompressible tree with infinitely many paths which does not compute any perfect path-incompressible tree with computable oracle-use.</p></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"297 ","pages":"Article 105136"},"PeriodicalIF":0.8000,"publicationDate":"2024-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Information and Computation","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0890540124000014","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"COMPUTER SCIENCE, THEORY & METHODS","Score":null,"Total":0}
引用次数: 0
Abstract
We study randomness-preserving transformations of path-incompressible trees, namely trees of finite randomness deficiency. We characterize their branching density, and show: (a) sparse perfect path-incompressible trees can be effectively densified, almost surely; (b) there exists a path-incompressible tree with infinitely many paths which does not compute any perfect path-incompressible tree with computable oracle-use.
期刊介绍：
Information and Computation welcomes original papers in all areas of theoretical computer science and computational applications of information theory. Survey articles of exceptional quality will also be considered. Particularly welcome are papers contributing new results in active theoretical areas such as
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Concurrency and distributed process theory-
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Design and analysis of algorithms-
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Inductive inference and learning theory-
Logic & constraint programming-
Program verification & model checking-
Probabilistic & Quantum computation-
Semantics of programming languages-
Symbolic computation, lambda calculus, and rewriting systems-
Types and typechecking
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