CS601 Syllabus Spring, 2021

Comp. Sci. 601

Syllabus

Spring, 2021

CMPSCI 601: Office Hours, Spring 2021
Neil Immerman, immerman@umass.edu	M, W 4 - 5, and by appointment.
Larkin Flodin, lflodin@cs.umass.edu	Th 4:30 - 5:30

Please check this syllabus frequently as it is here that I will post readings, problems, and other useful information. It is also subject to change. If there is a particular topic that you would like to know more about, please let me know early in the term. When I diverge from the text I will try to post notes or other sources here.

If some of the symbols that I have been using seem Greek to you, here is a Symbol Table to help you remember what they mean.

Supplementary Reading: -- not required, but I encourage you to read or skim any or all of these and please let me know if you have questions or comments.

Turing's orginal paper defining Turing machines: On Computable Numbers, With an Application to the Entscheidungsproblem," Proc. London Math. Soc., 2:42 (1936), 230-265.
An entry I wrote on Computability and Complexity, in Stanford Encyclopedia of Philosophy.
John Hopcroft, "Turing Machines" Scientific American, May 1984.
Arora & Barak: By the time of the midterm we will have completed most of Chapters 1 through 4. Of course I won't test you on anything we haven't covered in class.
Here are Chapters 0, 1 and 2, Chapter 4, Chapter 5 and Chapter 7 of my book, Descriptive Complexity.
A prerequisite for this course is an undergrad course on automata and formal languages such as COMPSCI 501. I recommend any of the following books if you want to review this material:
- Hopcroft, Motwani, Ullman, Introduction to Automata Theory, Languages, and Computation
- Lewis, Papadimitirou, Elements of The Theory of Computation
- Sipser, Theory of Computation

Note: This syllabus will be added to and updated as we go. If there is a topic you would really like to learn about, please let me know early.

Date Lecture Readings to be Completed Before Class (different text editions may have different section numbers, so use the topic names)

T, 2/2 1. Introduction and Turing Machines 0. "Introduction"

Th, 2/4 2. Recursive and r.e. sets and Busy Beaver 1. "Basic Complexity Classes"

T, 2/9 3. Reductions and r.e. Complete Sets

Th, 2/11 4. The Arithmetic Hierarchy and Intro to Complexity 2.1 - 2.2 "NP, Reducibility and NP Completeness"; HW1 due

T, 2/16 5. NP Completeness 2.3 "Cook-Levin Thm"

Th, 2/18 6. Descriptive Complexity and Fagin's Theorem Descriptive Complexity, Chapter 7

T, 2/23 7. Cook-Levin Theorem 2.4-2.6 "Reductions, Search, coNP, EXP, NEXP"

Th, 2/25 8. NSPACE and Savitch's Theorem 4.1 - 4.2 "Space Complexity, Savitch Thm" ; HW2 due

Tu, 3/2 9. Immerman-Szelepcsényi Theorem and PSPACE rest of Chapt. 4: "PSPACE and NL Completeness"

Th, 3/4 10. Space Hierarchy Theorem 3.1 - 3.2 "Hierarchy Thms"; HW3 due

Tu, 3/9 11. Ladner's Theorem & Oracles 3.3 "Ladner's Thm" & 3.4 "Oracles"

Th, 3/11 Take-Home Midterm

Tu, 3/16 12. Alternating Turing Machines "5.1 - 5.2 "PH"

Th, 3/18 13. Polynomial-Time Hierarchy 5.3 "Alternation"; Original Alternation Paper

Tu, 3/23 14. BPP and BPL 7.1 - 7.4 "Randomized Classes"

Th, 3/25 15. BPP is in PH rest of Chapt. 7 "More on Randomized Classes"; HW4 due

Tu, 3/30 16. Arthur Merlin Games 8.1-8.2 "IP & AM"

Th, 4/1 17. Shamir's Theorem 8.3 "IP = PSPACE"

Tu, 4/6 18. Circuit Complexity Chapt. 6 "Circuits"

Th, 4/8 19. CRAMS: Concurrent Parallel Random Access Machines Descriptive Complexity Chapt. 4; HW5 due

Tu, 4/13 20. NC¹ and Barrington's Theorem

Th, 4/15 21. Descriptive Complexity: Inductive Definitions and Parallel Classes Descriptive Complexity Chapt. 5

Th, 4/22 22. Quantum Computing 10.1 -- 10.5 "Quantum Computing"; HW6 due

Tu, 4/27 23. Schor's Algorithm rest of Chapt. 10

Th, 4/29 24. Håstad's Switching Lemma Hastad Switching Lemma

Tu, 5/4 25. Summary and Discussion

Date	Lecture	Readings to be Completed Before Class (different text editions may have different section numbers, so use the topic names)
T, 2/2	1. Introduction and Turing Machines	0. "Introduction"
Th, 2/4	2. Recursive and r.e. sets and Busy Beaver	1. "Basic Complexity Classes"

T, 2/9	3. Reductions and r.e. Complete Sets
Th, 2/11	4. The Arithmetic Hierarchy and Intro to Complexity	2.1 - 2.2 "NP, Reducibility and NP Completeness"; HW1 due

T, 2/16	5. NP Completeness	2.3 "Cook-Levin Thm"
Th, 2/18	6. Descriptive Complexity and Fagin's Theorem	Descriptive Complexity, Chapter 7

T, 2/23	7. Cook-Levin Theorem	2.4-2.6 "Reductions, Search, coNP, EXP, NEXP"
Th, 2/25	8. NSPACE and Savitch's Theorem	4.1 - 4.2 "Space Complexity, Savitch Thm" ; HW2 due

Tu, 3/2	9. Immerman-Szelepcsényi Theorem and PSPACE	rest of Chapt. 4: "PSPACE and NL Completeness"
Th, 3/4	10. Space Hierarchy Theorem	3.1 - 3.2 "Hierarchy Thms"; HW3 due

Tu, 3/9	11. Ladner's Theorem & Oracles	3.3 "Ladner's Thm" & 3.4 "Oracles"
Th, 3/11	Take-Home Midterm

Tu, 3/16	12. Alternating Turing Machines	"5.1 - 5.2 "PH"
Th, 3/18	13. Polynomial-Time Hierarchy	5.3 "Alternation"; Original Alternation Paper

Tu, 3/23	14. BPP and BPL	7.1 - 7.4 "Randomized Classes"
Th, 3/25	15. BPP is in PH	rest of Chapt. 7 "More on Randomized Classes"; HW4 due

Tu, 3/30	16. Arthur Merlin Games	8.1-8.2 "IP & AM"
Th, 4/1	17. Shamir's Theorem	8.3 "IP = PSPACE"

Tu, 4/6	18. Circuit Complexity	Chapt. 6 "Circuits"
Th, 4/8	19. CRAMS: Concurrent Parallel Random Access Machines	Descriptive Complexity Chapt. 4; HW5 due

Tu, 4/13	20. NC¹ and Barrington's Theorem
Th, 4/15	21. Descriptive Complexity: Inductive Definitions and Parallel Classes	Descriptive Complexity Chapt. 5

Th, 4/22	22. Quantum Computing	10.1 -- 10.5 "Quantum Computing"; HW6 due

Tu, 4/27	23. Schor's Algorithm	rest of Chapt. 10
Th, 4/29	24. Håstad's Switching Lemma	Hastad Switching Lemma

Tu, 5/4	25. Summary and Discussion