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CSCI 5444:
Theory of Computation
Logistics
- Instructor:
Ashutosh Trivedi (ashutosh \dot trivedi \at colorado \dot edu)
- Grading Assistant :
Krithika Balan (krithika \dot balan \at colorado \dot edu)
- Course description:
- Introduces the foundations of automata theory, computability
theory, and complexity theory.
- Shows relationship between automata and formal languages.
- Addresses the issue of which problems can be solved by
computational means (decidability vs undecidability), and
- Introduces concepts related to computational complexity of problems.
- Requisites:
- Discrete Structures/ Discrete Mathematics
- Undergraduate Algorithms
- Class Meeting Times: Tuesday (11:00am—12:15pm) and Thursday (11:00pm—12:15pm)
- Office hours:
- Ashutosh Trivedi (Monday 2pm—3pm), ECCS 122.
- Ashutosh Trivedi (Wednesday 12:15pm—1:15pm), over Zoom (for
Distance Section)
- Venue :
- Class meeting location: ECCS 1B28
- Office Hour location: ECCS 122
Relevant Textbooks
-
Required Text :
-
Other supplemental materials :
Assignments
- All assignments will be posted on moodle. Your identikey is needed for signing in.
Course Objectives
The objective of this course is provide an introduction to the
theory of computation covering the following three branches of theoretical computer science:
- Automata Theory
- Formalization of the notion of problems via formal languages
- Formalization of the notion of computation using "abstract computing devices" called automata
- Understanding a hierarchy of classes of problems or formal languages (regular, context-free, context-sensitive, decidable, and undecidable)
- Understanding a hierarchy of classes of automata (finite automata, pushdown automata, and Turing machines)
- Computability Theory
- Understanding Church-Turing thesis (Turing machines as a notion of "general-purpose computers")
- Understanding the concept of undecidability , i.e., when a problem can not be solved using computers
- How to show undecidability using the concept of problem reduction
- Complexity Theory
- Complexity classes : how to classify decidable problems based
on their time and space requirements
- Complexity classes P and NP
- Intractability (NP-completeness)
- How to prove NP-completeness?
- Complexity Classes PSPACE and PSPACE-completeness
Topics Covered
- Regular Languages (3 weeks)
- Deterministic finite-state machines
- Nondeterministic finite-state machines
- Regular expressions
- Properties of regular languages
- Languages that aren't regular: pumping lemma
- Context-Free Languages (2 weeks)
- Context-free grammars
- Pushdown automata
- Properties of Context-free languages
- Languages that aren't context-free: pumping lemma for CFLs
- Computability Theory (4 weeks)
- Turing machines and their variants
- Church-Turing thesis
- Decidable languages
- Undecidability
- Proving Undecidability of a given problem using problem
reductions
- Rice's theorem
- Famous undecidable problems such as Post Correspondence Problem
(PCP), Tiling problem, halting problems for multistack and
two-counter machines.
-
Complexity Theory (4 weeks)
- Time and space complexity
- Complexity classes P and NP, and NP-Completeness
- Famous NP-complete problems
- Complexity class PSPACE and Pspace-Completeness
- Complexity classes L and NL, and NL-completeness
- Advanced Topics for class projects (presentations in Week 16)
- Polynomial, exponential, and arithmetical hierarchies
- Approximation algorithms
- Probabilistic complexity
- Interactive proofs and complexity class IP
- Probabilistically checkable proofs
- Quantum algorithms (Dasgupta, Papadimitriou, and Vazirani)
- Alternation
- Automata on infinite words and S1S
- Timed and hybrid Automata
- Learning Finite Automata
- Markov Decision Processes
- Program termination analysis
Grading
The overall grade will be based on a cumulative score computed by adding
together the grades from:
- Weekly assignments (with least two scores omitted)
- In-class quizzes
- The final exam/project/presentations
- Class participation: you are expected to attend the class and to
regularly interact with the instructor in the class.
Schedule and Lecture Notes
# |
Date |
Description |
Chapter |
1 |
January 17 |
Introduction to the theory of computation
[Slides ]
|
0 |
Part One: Automata Theory
2 |
Week 1 — January 19 |
Regular languages and finite automata
[ Slides ]
|
1.1, 1.2 |
3 |
Week 2 — January 24 |
Deterministic Finite Automata
(Guest lecture by Dr. Sergio Mover)
|
1.2, 1.3 |
4 |
Week 2 — January 26 |
Nondeterministic Finite Automata
(Guest lecture by Dr. Sergio Mover)
|
1.3 |
5 |
Week 3 — January 31 |
Subset Construction: Nondeterminism and Alternation
[Slides ]
|
1.4 |
6 |
Week 3 — February 2 |
Regular expressions
|
|
7 |
Week 4 — February 6 |
Non-Regular languages: Pumping Lemma
[Slides ]
|
1.4 |
8 |
Week 4 — February 9 |
Context-Free Languages: Grammars and Derivations
|
2.1 |
9 |
Week 5 — February 14 |
Pushdown Automata
|
2.2 |
10 |
Week 5 — February 16 |
Non-Context-Free Languages
|
2.3 |
11 |
Week 6 — February 21 |
Closure properties of CFLs
|
|
12 |
Week 6 — February 23 |
Wrap-up of Regular Languages and CFLs
|
2.1 — 2.3 |
13 |
Week 7 — February 28 |
In-Class Quiz I
|
1 and 2 |
Part Two: Computability Theory
14 |
Week 7 — March 2 |
Turing machines
|
3.1 |
15 |
Week 8 — March 7 |
Variants of Turing machines
|
3.2 and 3.3 |
16 |
Week 8 — March 9 |
Decidability: Decidable Languages
|
4.1 |
17 |
Week 9 — March 14 |
Halting Problem: Diagonalization and Reductions
|
4.2 |
18 |
Week 9 — March 16 |
Reductions: More undecidable problems
|
5.1, 5.2 |
19 |
Week 10 — March 21 |
Logics and Decidability
|
6.2 |
20 |
Week 10 — March 23 |
Wrap-up: Turing machines and decidability
|
3-4-5-6 |
21 |
Week 11 — March 27-31 |
No Class — Spring Break
|
|
22 |
Week 12 — April 4 |
In-class Quiz II
|
3-4-5-6 |
Part Three: Complexity Theory
23 |
Week 12 — April 6 |
Complexity
|
7.1 and 7.2 |
24 |
Week 13 — April 11 |
NP, co-NP, polynomial-time reductions and NP-completeness
|
7.3 |
25 |
Week 13 — April 13 |
NP-complete problems and reductions
|
7.4 |
26 |
Week 14 — April 18 |
Space Complexity Classes: Savitch's theorem
|
|
27 |
Week 14 — April 20 |
PSPACE and PSPACE-complete problems
|
7 |
28 |
Week 15 — April 25 |
L, NL, and NL-completeness
|
8.4-8.6 |
29 |
Week 15 — April 27 |
In-class Quiz III
|
|
30 |
Week 16 — May 2 |
Class Project Presentations
|
|
31 |
Week 16 — May 4 |
Class Project Presentations
|
|
Notes
-
Accommodation Statement.
If you qualify for accommodations because of a disability, please submit to me a
letter from Disability Services in a timely manner (for exam accommodations
provide your letter at least one week prior to the exam) so that your needs can
be addressed. Disability Services determines accommodations based on documented
disabilities. Contact Disability Services at 303-492-8671 or by e-mail at dsinfo
[AT] colorado.edu.
If you have a temporary medical condition or injury, see Temporary Injuries
under Quick Links at the Disability Services website and discuss your needs with
me.
-
Religious Observances.
Campus policy regarding religious observances requires that faculty make every
effort to deal reasonably and fairly with all students who, because of religious
obligations, have conflicts with scheduled exams, assignments or required
attendance. In this class, you should notify your instructor of any conflict at
least two weeks in advance. See full details
here .
-
Classroom Behavior.
Students and faculty each have responsibility for maintaining an appropriate
learning environment. Those who fail to adhere to such behavioral standards may
be subject to discipline. Professional courtesy and sensitivity are especially
important with respect to individuals and topics dealing with differences of
race, color, culture, religion, creed, politics, veteran's status, sexual
orientation, gender, gender identity and gender expression, age, disability, and
nationalities. Class rosters are provided to the instructor with the student's
legal name. I will gladly honor your request to address you by an alternate name
or gender pronoun. Please advise me of this preference early in the semester so
that I may make appropriate changes to my records. For more information, see the
policies
on
classroom behavior and
the
student code.
-
Discrimination and Harassment.
The University of Colorado Boulder (CU Boulder) is committed to maintaining a
positive learning, working, and living environment. CU Boulder will not tolerate
acts of sexual misconduct, discrimination, harassment or related retaliation
against or by any employee or student. CU's Sexual Misconduct Policy prohibits
sexual assault, sexual exploitation, sexual harassment, intimate partner abuse
(dating or domestic violence), stalking or related retaliation. CU Boulder's
Discrimination and Harassment Policy prohibits discrimination, harassment or
related retaliation based on race, color, national origin, sex, pregnancy, age,
disability, creed, religion, sexual orientation, gender identity, gender
expression, veteran status, political affiliation or political
philosophy. Individuals who believe they have been subject to misconduct under
either policy should contact the Office of Institutional Equity and Compliance
(OIEC) at 303-492-2127. Information about the OIEC, the above referenced
policies, and the campus resources available to assist individuals regarding
sexual misconduct, discrimination, harassment or related retaliation can be
found at
the OIEC website.
-
Honor Code.
All students enrolled in a University of Colorado Boulder course are responsible
for knowing and adhering to
the academic
integrity policy of the
institution. Violations of the policy may include: plagiarism, cheating,
fabrication, lying, bribery, threat, unauthorized access, clicker fraud,
resubmission, and aiding academic dishonesty. All incidents of academic
misconduct will be reported to the Honor Code Council (honor@colorado.edu;
303-735-2273). Students who are found responsible for violating the academic
integrity policy will be subject to nonacademic sanctions from the Honor Code
Council as well as academic sanctions from the faculty member. Additional
information regarding the academic integrity policy can be found at
honorcode.colorado.edu.
- The web-page of a previous offering of the course is available here .