国际著名的控制理论专家、加拿大皇家科学院院士、IEEE终身院士（life fellow）、美国工程院外籍院士、加拿大多伦多大学W. M. Wonham教授，将于今年夏学期来控制系开设名为“ALGEBRA FOR FORMAL LANGUAGES AND AUTOMATA”的课程（选课系统里的课程名称沿用老的课程名《离散事件系统监控理论》，课程号111330501），该课程面向研究生和高年级的本科生，侧重于逻辑思维方法的训练。现继续开放选课。由于选课系统已经关闭，请欲选课者把您的姓名和学号发给魏勇同学（邮件ywei@iipc.zju.edu.cn）或者瞿新泉同学（04dzjsqxq@gmail.com），我们将在后台操作，为您补选。截至时间为下周一（3月21日）上班前。


附课程大纲：
ALGEBRA FOR FORMAL LANGUAGES AND AUTOMATA

W.M. Wonham
Professor Emeritus, ECE
University of Toronto
wonham@control.utoronto.ca

This course is intended for final-year undergraduates and first-year graduate students in systems and control. The primary objective is to introduce some of the basic algebraic ideas underlying regular languages and finite automata, with possible applications to supervisory control of discrete-event systems. A secondary objective is to provide practice in 'formal thinking' for students whose previous exposure to mathematics has been largely of an applied engineering flavor. Thus a careful and rigorous, though elementary, approach will be emphasized. There are no particular mathematical prerequisites. The syllabus (time permitting) is as follows.

1. Sets and functions
2. Partially ordered sets (posets)
3. Lattices - basics
4. Distributive lattices and Boolean algebras
5. Lattice of equivalence relations
6. Equivalence kernel and canonical factorization
7. Congruences of dynamic systems
8. Application: Internal Model Principle of regulation theory.
9. Formal languages
10. Nerode equivalence and right congruence
11. Canonical recognizers
12. Generators
13. Chains of regular languages
14. Supports and chain convergence of regular languages
15. Natural projection
16. Synchronous product of languages and generators
17. Natural projections and normal languages
18. Observable languages
19. Natural observers
20. Nondeterminism, quasi-congruences and the observer property

Schedule:
The lectures will be presented in the 7-week period starting Monday April 25 and finishing Friday June 17. Normally there will be a total of 3 lecture hours per week. Office time will be available for tutorial help.
Lesson 1: Tuesday afternoon: 14:55-16:40
Lesson 2: Thursday afternoon: 13:15-14:50
CSC Room 223

Obligation:
There will be weekly homework to be handed in, and a final problem set for grading. The period Friday June 10 to Wednesday June 15 will be available for a final assignment and project.

Teaching assistants:
1. QU Xinquan (04dzjsqxq@gmail.com)
2. WEI Yong (ywei@iipc.zju.edu.cn)

References:
[1] S. MacLane, G. Birkhoff. Algebra. Third edition, Chelsea, 1993. （Ch. 1, Sets, Functions, and Integers, pp.1-42; Ch. 4, Universal Constructions, Sect. 4.6, Posets and Lattices, pp.143-146; Ch. 14, Lattices, pp.470-494.）
[2] W.M. Wonham. Supervisory Control of Discrete-Event Systems. ECE Dept., U. of Toronto.
[3] Design software XPTCT. ECE Dept., U. of Toronto, update 201107.01. (The material needed from [1] will be provided in class, while [2] and [3] will be distributed electronically.

Other sources with helpful background material include the following.
[4] I.N. Herstein. Topics in Algebra (Ch. 1, Preliminary Notions. Set theory, Mappings, The Integers, pp.1-24.)
[5] D.M. Burton. Abstract Algebra. (Ch. 1, Preliminary Notions. The Algebra of Sets, Functions and Relations, Elementary Number Theory, pp.1-43.)
[6] D. Solow. How to Read and Do Proofs. (Ch. 12, Summary, pp.92-99.)
[7] B.A. Davey, H.A. Priestley. Introduction to Lattices and Order. (Ch. 1, Ordered sets; Ch. 2, Lattices and complete lattices.)