Wadge degrees of Δ 2 0 $\mathbf{\Delta }^0_2$ omega-powers

Pub Date : 2024-09-06 DOI:10.1002/malq.202400024

Olivier Finkel, Dominique Lecomte

{"title":"Wadge degrees of \n \n \n Δ\n 2\n 0\n \n $\\mathbf{\\Delta }^0_2$\n omega-powers","authors":"Olivier Finkel, Dominique Lecomte","doi":"10.1002/malq.202400024","DOIUrl":null,"url":null,"abstract":"We provide, for each natural number <math>\n <semantics>\n <mi>n</mi>\n <annotation>$n$</annotation>\n </semantics></math> and each class among <math>\n <semantics>\n <mrow>\n <msub>\n <mi>D</mi>\n <mi>n</mi>\n </msub>\n <mrow>\n <mo>(</mo>\n <msubsup>\n <mi>Σ</mi>\n <mn>1</mn>\n <mn>0</mn>\n </msubsup>\n <mo>)</mo>\n </mrow>\n </mrow>\n <annotation>$D_n(\\mathbf {\\Sigma }^0_1)$</annotation>\n </semantics></math>, <math>\n <semantics>\n <mrow>\n <msub>\n <mover>\n <mi>D</mi>\n <mo>̌</mo>\n </mover>\n <mi>n</mi>\n </msub>\n <mrow>\n <mo>(</mo>\n <msubsup>\n <mi>Σ</mi>\n <mn>1</mn>\n <mn>0</mn>\n </msubsup>\n <mo>)</mo>\n </mrow>\n </mrow>\n <annotation>$\\check{D}_n(\\mathbf {\\Sigma }^0_1)$</annotation>\n </semantics></math>, <math>\n <semantics>\n <mrow>\n <msub>\n <mi>D</mi>\n <mrow>\n <mn>2</mn>\n <mi>n</mi>\n <mo>+</mo>\n <mn>1</mn>\n </mrow>\n </msub>\n <mrow>\n <mo>(</mo>\n <msubsup>\n <mi>Σ</mi>\n <mn>1</mn>\n <mn>0</mn>\n </msubsup>\n <mo>)</mo>\n </mrow>\n <mi>⊕</mi>\n <msub>\n <mover>\n <mi>D</mi>\n <mo>̌</mo>\n </mover>\n <mrow>\n <mn>2</mn>\n <mi>n</mi>\n <mo>+</mo>\n <mn>1</mn>\n </mrow>\n </msub>\n <mrow>\n <mo>(</mo>\n <msubsup>\n <mi>Σ</mi>\n <mn>1</mn>\n <mn>0</mn>\n </msubsup>\n <mo>)</mo>\n </mrow>\n </mrow>\n <annotation>$D_{2n+1}(\\mathbf {\\Sigma }^0_1)\\oplus \\check{D}_{2n+1}(\\mathbf {\\Sigma }^0_1)$</annotation>\n </semantics></math>, a regular language whose associated omega-power is complete for this class.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/malq.202400024","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 0

Abstract

We provide, for each natural number $n$ and each class among $D_{n} (Σ_{1}^{0})$ , ${\overset{̌}{D}}_{n} (Σ_{1}^{0})$ , $D_{2 n + 1} (Σ_{1}^{0}) \oplus {\overset{̌}{D}}_{2 n + 1} (Σ_{1}^{0})$ , a regular language whose associated omega-power is complete for this class.

查看原文

Δ20$mathbf\{Delta }^0_2$ Ω-幂的瓦奇度

我们为每个自然数和ⅣⅤ类中的每个类提供一种正则表达式语言，其相关的Ω-幂对该类来说是完整的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文