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 計算理論 Theory of Computation

(Spring 2024)

Instructor: 顏嗣鈞
E-mail:  hcyen(_at_)ntu.edu.tw

Time:  2:20-5:20 PM, Tuesday

Place: Room BL-112

Office phone: (02) 3366 3581

Office hours: by appointment

TA:  王璲  博理館606室      

     (02) 33663700 ext 6606    

        D07921012@ntu.edu.tw 


Announcements:


Class Notes:  

This course provides a rigorous, graduate level introduction to Automata theory, Formal languages, and Complexity. Topics to be covered will include:

 

Topics

  Chapter 0 Introduction and mathematical notations Intro.pdf

(updated 2/18)

 
Chapter 1  Regular  Languages
  • deterministic vs. nondeterministic FA,
  • minimization
  • pumping lemma for regular sets,
  • closure properties,
  • decision properties,
  • Myhill-Nerode theorem ...
Chap1.pdf (updated 3/4)

Supplementary materials

Chapter 2 Context-free  Languages
  • deterministic vs. nondeterministic PDA,
  • one-way vs. two-way PDA,
  • reversal   bounded PDA,
  • linear grammars,
  • counter machines,
  • pumping lemma for CFLs,
  • Chomsky normal form,   
  • Greibach normal form,
  • closure properties, ...
Chap2.pdf

(updated 3/25)

Chapter 3

 

The Church-Turing Thesis

Decidability

  • variants of Turing machines,
  • halting problem,
  • undecidability,  
  • valid and invalid computations of TMs
Chap3.pdf
Chapter 4 Reducibility
  • Reductions
  • Undecidability proof
  • Post correspondence problem,
  • Basic recursive function theory, ...
Chap4.pdf

(updated 4/25)

Supplementary materials

Chapter 5 Complexity Theory
  • various resource bounded complexity classes, including NLOGSPACE, P, NP, PSPACE, EXPTIME, and many more,
  • reducibility,  
  • completeness, ...
  • time/space hierarchy theorems
  • probabilistic complexity classes
 
Chap5.pdf

(updated 5/13) 

Probabilistic Computation

(updated 5/19) 

Oracle Computation and Polynomial-Time Hierarchy

 

Decision vs. Search

 

 

 

 

 

 

Reference textbook:

  • Introduction to the Theory of Computation,  Michael Sipser, (3rd Ed. Thomson) 開發圖書


Grading:  

  • Homework: 20%

  • Midterm exam: 40%

  • Final exam:  40% 

 

 

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