Comp. Sci. 601 Syllabus Spring, 2021

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

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 Complexity2.1 - 2.2 "NP, Reducibility and NP Completeness"; HW1 due
T, 2/16 5. NP Completeness2.3 "Cook-Levin Thm"
Th, 2/18 6. Descriptive Complexity and Fagin's Theorem Descriptive Complexity, Chapter 7
T, 2/23 7. Cook-Levin Theorem2.4-2.6 "Reductions, Search, coNP, EXP, NEXP"
Th, 2/25 8. NSPACE and Savitch's Theorem4.1 - 4.2 "Space Complexity, Savitch Thm" ; HW2 due
Tu, 3/2 9. Immerman-Szelepcsényi Theorem and PSPACErest 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 Hierarchy5.3 "Alternation"; Original Alternation Paper
Tu, 3/23 14. BPP and BPL7.1 - 7.4 "Randomized Classes"
Th, 3/25 15. BPP is in PHrest 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 Theorem8.3 "IP = PSPACE"
Tu, 4/6 18. Circuit ComplexityChapt. 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, 4/1521. Descriptive Complexity: Inductive Definitions and Parallel ClassesDescriptive Complexity Chapt. 5
Th, 4/22 22. Quantum Computing10.1 -- 10.5 "Quantum Computing"; HW6 due
Tu, 4/27 23. Schor's Algorithmrest of Chapt. 10
Th, 4/29 24. Håstad's Switching LemmaHastad Switching Lemma
Tu, 5/425. Summary and Discussion