Concurrency Theory and Non-Numerical Approximation

并发理论和非数值近似

• 批准号: RGPIN-2015-06466
• 负责人: Janicki, Ryszard
• 金额: $ 1.75万
• 依托单位: McMaster University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2016
• 资助国家: 加拿大
• 起止时间: 2016-01-01 至 2017-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=614170
• 关键词: Concurrency; Theory; Non; Numerical; Approximation

Both concurrent systems and approximation problems abound in human experience but their fully adequate conceptualization as yet eludes us. Our increasing dependence on ever more complex systems in the management and control of human affairs and activities increases the urgency for developing more adequate and preferable more formal concepts to maintain reliable control over systems we have created. The solution of the problem of correct specification of the design and verification of its behaviour becomes crucial, and a satisfactory conceptual apparatus for rigorous specification and verification becomes essential. The project will explore theoretical issues involved in the formal reasoning about concurrent systems and approximate reasoning. First general aim is to develop a framework, based on the concept of Generalized Causality modelled by Discrete Relational Structures (developed by Janicki and Koutny) and generalization of Mazurkiewicz traces, to support the design and the verification of sophisticated concurrent systems. The second general aim is to strengthen foundations and improve applications of non-numerical approximation and non-numerical ranking techniques. What connects all three topics is methodology, as the scientific method is basically the same, i.e., discrete mathematics, especially set, relation and automata theory and of course formal logic.

并行系统和近似问题在人类经验中都很丰富，但它们的充分概念化至今仍未得到我们的理解。我们在管理和控制人类事务和活动方面越来越依赖越来越复杂的系统，因此迫切需要制定更充分、更可取的更正式的概念，以维持对我们创建的系统的可靠控制。 解决正确规范设计和验证其行为的问题变得至关重要，而一个令人满意的严格规范和验证的概念性设备变得至关重要。 该项目将探索关于并发系统和近似推理的形式推理所涉及的理论问题。第一个总体目标是开发一个框架，该框架基于离散关系结构(由Janicki和Koutny提出)和Mazurkiewicz迹的推广的广义因果关系的概念，以支持复杂并发系统的设计和验证。第二个总体目标是加强非数值逼近和非数值排序技术的基础和改进应用。 连接这三个主题的是方法论，因为科学方法基本上是相同的，即离散数学，特别是集合、关系和自动机理论，当然还有形式逻辑。