Pub Date : 1900-01-01DOI: 10.1142/9789812562494_0069
C. Martín-Vide, A. Paun, G. Paun
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Pub Date : 1900-01-01DOI: 10.1142/9789812562494_0044
A. Blass, Y. Gurevich
One of the previous articles in this column was devoted to the zero-one laws for a number of logics playing prominent role in finite model theory: first-order logic FO, the extension FO+LFP of first-order logic with the least fixed-point operator, and the infinitary logic L∞,ω. Recently Shelah proved a new, powerful, and surprising zero-one law. His proof uses so-called strong extension axioms. Here we formulate Shelah’s zero-one law and prove a few facts about these axioms. In the process we give a simple proof for a “large deviation” inequality a la Chernoff. 1 Shelah’s Zero-One Law Quisani: What are you doing, guys? Author: We2 are proving a zero-one law which is due to Shelah. Q: Didn’t Shelah prove the law? A: Oh yes, he proved it all right, and even wrote it down [14]. Q: So what is the problem? Can’t you read his proof? 1Mathematics, University of Michigan, Ann Arbor, MI 48109-1109, USA; partially supported by a grant from Microsoft Research. 2The record of the conversation was simplified by blending the two authors into one who prefers “we” to “I”.
{"title":"A New Zero-One Law and Strong Extension Axioms","authors":"A. Blass, Y. Gurevich","doi":"10.1142/9789812562494_0044","DOIUrl":"https://doi.org/10.1142/9789812562494_0044","url":null,"abstract":"One of the previous articles in this column was devoted to the zero-one laws for a number of logics playing prominent role in finite model theory: first-order logic FO, the extension FO+LFP of first-order logic with the least fixed-point operator, and the infinitary logic L∞,ω. Recently Shelah proved a new, powerful, and surprising zero-one law. His proof uses so-called strong extension axioms. Here we formulate Shelah’s zero-one law and prove a few facts about these axioms. In the process we give a simple proof for a “large deviation” inequality a la Chernoff. 1 Shelah’s Zero-One Law Quisani: What are you doing, guys? Author: We2 are proving a zero-one law which is due to Shelah. Q: Didn’t Shelah prove the law? A: Oh yes, he proved it all right, and even wrote it down [14]. Q: So what is the problem? Can’t you read his proof? 1Mathematics, University of Michigan, Ann Arbor, MI 48109-1109, USA; partially supported by a grant from Microsoft Research. 2The record of the conversation was simplified by blending the two authors into one who prefers “we” to “I”.","PeriodicalId":388781,"journal":{"name":"Bull. EATCS","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125303977","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1900-01-01DOI: 10.1142/9789812562494_0054
J. Srba
This paper provides a comprehensive summary of equivalence checking results for infinite-state systems. References to the relevant papers will be updated continuously according to the development in the area. The most recent version of this document is available from the web-page http://www.brics.dk/~srba/roadmap.
{"title":"Roadmap of Infinite Results","authors":"J. Srba","doi":"10.1142/9789812562494_0054","DOIUrl":"https://doi.org/10.1142/9789812562494_0054","url":null,"abstract":"This paper provides a comprehensive summary of equivalence\u0000checking results for infinite-state systems. References to the\u0000relevant papers will be updated continuously according to the\u0000development in the area. The most recent version of this\u0000document is available from the web-page\u0000http://www.brics.dk/~srba/roadmap.","PeriodicalId":388781,"journal":{"name":"Bull. EATCS","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121329455","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1900-01-01DOI: 10.4135/9781473915077.n19
L. Priese
Copyright: Alle Rechte vorbehalten. Die verwendeten Texte, Bilder und Grafiken sowie das Layout dieser Seiten unterliegen weltweitem Urheberrecht. Die unerlaubte Verwendung, Reproduktion oder Weitergabe einzelner Inhalte oder kompletter Seiten ist untersagt. Dies gilt ebenso für die unerlaubte Einbindung einzelner Inhalte oder kompletter Seiten auf Websites anderer BetreiberInnen. Das Einrichten von Links auf diese Website ist jedoch ausdrücklich gestattet. Überblick Fairness
{"title":"Fairness","authors":"L. Priese","doi":"10.4135/9781473915077.n19","DOIUrl":"https://doi.org/10.4135/9781473915077.n19","url":null,"abstract":"Copyright: Alle Rechte vorbehalten. Die verwendeten Texte, Bilder und Grafiken sowie das Layout dieser Seiten unterliegen weltweitem Urheberrecht. Die unerlaubte Verwendung, Reproduktion oder Weitergabe einzelner Inhalte oder kompletter Seiten ist untersagt. Dies gilt ebenso für die unerlaubte Einbindung einzelner Inhalte oder kompletter Seiten auf Websites anderer BetreiberInnen. Das Einrichten von Links auf diese Website ist jedoch ausdrücklich gestattet. Überblick Fairness","PeriodicalId":388781,"journal":{"name":"Bull. EATCS","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134341975","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1900-01-01DOI: 10.1142/9789812562494_0013
Ronen Shaltiel
Extractors are functions which are able to “extract” random bits from arbitrary distributions which “contain” sufficient randomness. Explicit constructions of extractors have many applications in complexity theory and combinatorics. This manuscript is a survey of recent developments in extractors and focuses on explicit constructions of extractors following Trevisan’s breakthrough result [Tre99].
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This contribution is intended to be a self-contained and minimally technical exposition of the material in my 2015 dissertation, which was supervised by Markus Blaser. As its title suggests, the thesis investigates the complexity of combinatorial counting problems in the frameworks of parameterized (and exponential-time) complexity. More precisely, the following specific settings are explored: Counting perfect matchings in structurally “simple” graphs, for instance, in graphs that exclude specific fixed minors Counting small subgraph patterns in large host graphs Exponential lower bounds on the running time needed to solve counting problems, assuming popular conjectures such as the exponentialtime hypothesis
这篇论文旨在对我 2015 年论文中的材料进行自足且技术性极低的阐述，该论文由 Markus Blaser 指导。正如论文题目所示，论文在参数化（和指数时间）复杂性的框架内研究了组合计数问题的复杂性。更确切地说，论文探讨了以下具体情况：在结构 "简单 "的图中计算完全匹配，例如在排除特定固定小数的图中 计算大型主图中的小子图模式 假设流行的猜想（如指数时间假设），求解计数问题所需的运行时间的指数下限
{"title":"The simple, little and slow things count: on parameterized counting complexity","authors":"Radu Curticapean","doi":"10.22028/D291-26612","DOIUrl":"https://doi.org/10.22028/D291-26612","url":null,"abstract":"This contribution is intended to be a self-contained and minimally technical exposition of the material in my 2015 dissertation, which was supervised by Markus Blaser. As its title suggests, the thesis investigates the complexity of combinatorial counting problems in the frameworks of parameterized (and exponential-time) complexity. More precisely, the following specific settings are explored: Counting perfect matchings in structurally “simple” graphs, for instance, in graphs that exclude specific fixed minors Counting small subgraph patterns in large host graphs Exponential lower bounds on the running time needed to solve counting problems, assuming popular conjectures such as the exponentialtime hypothesis","PeriodicalId":388781,"journal":{"name":"Bull. EATCS","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134207252","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1900-01-01DOI: 10.1142/9789812562494_0026
M. Hirvensalo
{"title":"Some Open Problems Related to Quantum Computing","authors":"M. Hirvensalo","doi":"10.1142/9789812562494_0026","DOIUrl":"https://doi.org/10.1142/9789812562494_0026","url":null,"abstract":"","PeriodicalId":388781,"journal":{"name":"Bull. EATCS","volume":"94 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134043977","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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