理论计算机科学中的几个问题.pptVIP

理论计算机科学中的几个问题 应明生 清华大学计算机科学与技术系 智能技术与系统国家重点实验室 EATCS(欧洲理论计算机科学协会)： 主办杂志： Theoretical Computer Science 主办会议：ICALP (International Colloquim on Automata, Languages, and Programming) “Theoretical Computer Science is mathematical and abstract in spirit, but it derives its motivations from practical and everyday computation. Its aim is to understand the nature of computation and, as a consequence of this understanding, provide more efficient methodologies.” Section A: Algorithms, automata, complexity and games Section B: Logic, semantics and theory of programming Section C: Natural computing (evolutionary computing, neural network, molecular computring, quantum computing, …) 美国的理论计算机科学： ACM STOC, IEEE FOCS 算法与复杂性， 人工智能理论（如 Logical AI） 欧洲的理论计算机科学： 形式化方法， 形式语义学， … 我国在理论计算机科学（包括美式、欧 式）方面有许多非常出色的工作 如何进一步发展我国的理论计算机科学？ P. R. Halmos: “问题是数学的心脏” 推而广之： “问题是一切（纯）科学的心 脏” 发展理论计算机科学，我们需要好的问题！ 波兰（华沙、里沃夫）数学学派的启示： 有自己特色的、根本性的问题 有与国际上同类工作相同的深度 问题1： 可否建立基于量子逻辑（或其它非 经典逻辑）的计算理论？是否需要建 立这样的理论？ An axiomatization of a mathematical theory consists of a system of fundamental notions as well as a set of axioms about these notions A mathematical theory is then the set of theorems which can be derived from the axioms One needs a certain logic to provide tools for reasoning in the derivation of these theorems from the axioms A. Heyting (1963), Axiomatic Projective Geometry, North-Holland, Amsterdam, 1963 In elementary axiomatics logic was used in an unanalyzed form The studies for foundations of mathematics beginning in the early of twentieth century: It had been realized that a major part of mathematics has to exploit the full power of classical (Boolean) logic, the strongest one in the family of existing logics A few mathematicians took some kind of constructive position which is in more or less explicit opposition to certain forms of mathematical reasoning used by the ma