Logic and Computability

逻辑和可计算性

基本信息

  • 批准号:
    9802843
  • 负责人:
  • 金额:
    --
  • 依托单位:
  • 依托单位国家:
    美国
  • 项目类别:
    Continuing grant
  • 财政年份:
    1998
  • 资助国家:
    美国
  • 起止时间:
    1998-07-01 至 2001-09-30
  • 项目状态:
    已结题

项目摘要

The proposed project includes research into a broad range of topics in computability theory (recursion theory) and logic, both theoretical and applied to other areas of mathematics and computer science. Included in the first area are investigations of the structures of sets and functions ordered by different notions of relative complexity of computation. Particular emphasis will be placed on the complexity structures of sets which are effectively enumerable and on the most general notion of relative computability as defined by unrestricted Turing machine computations. Computation procedures that place effective bounds on the access to oracle information or the run time of the computations will also be investigated, as well as reductions between real numbers based on the relative rates of convergence of effective approximations to the real numbers. Applications of the methods of pure computability theory will be made in the areas of computable algebra and model theory. The second area includes the study of structures representable by finite automata, decision procedures, the analysis and development of nonmonotonic logic, concurrent programming models, and applications of linear programming ideas and algorithms to data structures and logic programming. A primary focus here will be the logical and mathematical foundations of hybrid (continuous and discrete) control theory as well as the practical implementation of algorithms for these subjects based on the theoretical work being done.The work proposed in the first area is directed at a better understanding of the fundamental notions of computability and relative difficulty of computation for different tasks. The theoretical work deals both with the abstract notions of computability as well as with applications to specific branches of, and questions in, other areas of mathematics. One important application (within mathematics) concerns the general question of what starting information is needed to be able to compute other aspects of many important classes of mathematical structures. In practical terms, the results at times indicate that there are no algorithms for certain important tasks or that more information than might have been expected is needed to write programs calculating the desired results. The second area deals more directly with developing the mathematical (and especially logical) tools needed for the crucial areas of program verification, data management, and automated control of real-world complex systems. Commercial applications are expected for some of this work and there has already been a spin off to a start-up company developing several applications including data compression and network management algorithms.
拟议的项目包括研究可计算性理论(递归理论)和逻辑的广泛主题,包括理论和应用于数学和计算机科学的其他领域。包括在第一个领域的调查结构的集合和功能排序的不同概念的相对复杂性的计算。 特别强调将放在复杂性结构的集,这是有效的可计算性和最一般的概念,相对可计算性定义的不受限制的图灵机计算。 计算程序,放置有效的界限上的访问Oracle信息或运行时间的计算也将进行调查,以及减少之间的真实的数字的基础上的相对速度收敛的有效近似的真实的数字。纯可计算性理论方法的应用将在可计算代数和模型论领域进行。第二个领域包括研究可由有限自动机表示的结构,决策程序,非单调逻辑的分析和发展,并发编程模型,以及线性规划思想和算法在数据结构和逻辑编程中的应用。这里的主要重点是混合(连续和离散)控制理论的逻辑和数学基础,以及基于正在进行的理论工作的这些主题的算法的实际实现。第一个领域提出的工作旨在更好地理解可计算性的基本概念和不同任务的相对计算难度。理论工作涉及的抽象概念的可计算性,以及与应用程序的具体分支,和问题,其他领域的数学。一个重要的应用(在数学中)涉及的一般问题是,需要什么样的起始信息才能计算许多重要类别的数学结构的其他方面。实际上,结果有时表明,某些重要任务没有算法,或者需要比预期更多的信息来编写计算所需结果的程序。第二个领域更直接地涉及开发程序验证,数据管理和现实世界复杂系统的自动控制等关键领域所需的数学(特别是逻辑)工具。预计其中一些工作将用于商业应用,并且已经有一家初创公司开发了几种应用程序,包括数据压缩和网络管理算法。

项目成果

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Richard Shore其他文献

Richard Shore的其他文献

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{{ truncateString('Richard Shore', 18)}}的其他基金

Logic and Computability
逻辑和可计算性
  • 批准号:
    1161175
  • 财政年份:
    2012
  • 资助金额:
    --
  • 项目类别:
    Continuing Grant
[Environment] WILDCOMS-Wildlife Disease & Contaminant Monitoring & Surveillance Network
[环境] WILDCOMS-野生动物疾病
  • 批准号:
    NE/I021063/1
  • 财政年份:
    2011
  • 资助金额:
    --
  • 项目类别:
    Research Grant
Logic and Computability
逻辑和可计算性
  • 批准号:
    0852811
  • 财政年份:
    2009
  • 资助金额:
    --
  • 项目类别:
    Standard Grant
Logic and Computability
逻辑和可计算性
  • 批准号:
    0554855
  • 财政年份:
    2006
  • 资助金额:
    --
  • 项目类别:
    Continuing Grant
Logic and Computability
逻辑和可计算性
  • 批准号:
    0100035
  • 财政年份:
    2001
  • 资助金额:
    --
  • 项目类别:
    Continuing Grant
Complexity in the Constructive and Intuitionistic Theory of Reals
实数建构性直觉理论的复杂性
  • 批准号:
    9704337
  • 财政年份:
    1997
  • 资助金额:
    --
  • 项目类别:
    Standard Grant
Computability, Logic and Complexity
可计算性、逻辑性和复杂性
  • 批准号:
    9602579
  • 财政年份:
    1997
  • 资助金额:
    --
  • 项目类别:
    Standard Grant
Mathematical Sciences: Logic and Computability
数学科学:逻辑与可计算性
  • 批准号:
    9503503
  • 财政年份:
    1995
  • 资助金额:
    --
  • 项目类别:
    Continuing grant
Support for Latin American Symposium on Mathematical Logic; Bahia Blanca, Argentina; July 1992
支持拉丁美洲数理逻辑研讨会;
  • 批准号:
    9123305
  • 财政年份:
    1992
  • 资助金额:
    --
  • 项目类别:
    Standard Grant
Mathematical Sciences: Meeting: Logical Methods in Mathematics and Computer Science
数学科学:会议:数学和计算机科学中的逻辑方法
  • 批准号:
    9203905
  • 财政年份:
    1992
  • 资助金额:
    --
  • 项目类别:
    Standard Grant

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Computability theory on intuitionistic logic and its application to constructive reverse mathematics
直觉逻辑的可计算性理论及其在构造性逆向数学中的应用
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Logic and Computability
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  • 批准号:
    0100035
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    9802619
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    1998
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Computability, Logic and Complexity
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    9503503
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