Formal Foundations for Teaching Support Systems in Theoretical Computer Science

理论基础是计算机科学各种应用的支柱。硬件和软件的正确性是通过源自自动机理论和逻辑的形式化方法来验证的；从现代数据库中提取信息依赖于我们对逻辑和复杂性理论基础的理解；智能系统中的知识和推理的表示也需要坚实的理论基础。因此，现代技术辅助的计算机科学理论基础--逻辑基础、形式语言理论、复杂性理论和可计算性理论--及其方法的教学对未来的计算机科学家具有重要意义。然而，为理论计算机科学教育构建技术，帮助学生提供个性化的、精心设计的反馈，并帮助教师进行高质量的进度分析，是一项具有挑战性的任务，在许多情况下，这需要理论计算机科学本身提供新的复杂方法和工具。本项目的目标是(A)系统地确定和形式化理论计算机科学教学支持系统中出现的理论挑战；(B)通过用现有或新开发的理论方法来探索和解决这些挑战，为这些挑战提供概念性解决方案。开发的方法应集成到理论计算机科学的教学支持系统中。

Theoretical foundations are the backbone of diverse applications of computer science. Correctness of hardware and software is verified with formal methods originating from automata theory and logics; information extraction from modern databases relies on our understanding of the foundations of logics and complexity theory; and also representation of knowledge and inference in intelligent systems requires a solid theoretical basis. Modern, technology-assisted teaching of the foundations of theoretical computer science -- basics in logic, formal language theory, complexity theory, and computability theory -- as well as its methods, thus, has high significance for future computer scientists. Yet building technology for theoretical computer science education that assists students with individualized, well-designed feedback and instructors with high-quality analyses of progress is a challenging task, which in many cases requires new sophisticated methods and tools from theoretical computer science itself. The goal of this project is (A) to systematically identify and formalize theoretical challenges arising in the context of teaching support systems for theoretical computer science; and (B) to provide conceptual solutions to these challenges by exploring and addressing them with existing or newly-developed theoretical methods. The developed methods shall be integrated prototypically into a teaching support system for theoretical computer science.