Time

TTh 2–3:15pm

Location

127 Hayes-Healy

Instructor

David Chiang

Prerequisites

Discrete Mathematics (CSE 20110) or equivalent. You especially need to be comfortable with sets, tuples, functions, relations, and graphs; and writing proofs by contradiction and by induction.

Data Structures (CSE 20311) is recommended but not required for group programming assignments. If you haven't taken this course or equivalent, you may want to join a group with students who have.

Required text

Michael Sipser, Introduction to the Theory of Computation
3rd International Edition
ISBN: 9781133187813, 9788131525296
Price: usually $15–20 (Amazon)
Why this is legal
Errata

Description

Introduction to formal languages and automata, computability theory, and complexity theory with the goal of developing understanding of the power and limits of different computational models. Topics covered include:

• regular languages and finite automata
• context-free grammars and pushdown automata
• Turing machines; undecidable languages
• the classes P and NP; NP completeness

Links

The following sites will be used in this course:

• Notes and assignments will be linked from here, but you can also clone the GitHub repository
• Campuswire for questions and answers
• Canvas for submitting and grading assignments

Notes are posted as Colab notebooks. You should be able to use them in your browser, but if you want to use them on your own machine, install Tock, clone the Git repository, and run jupyter notebook in your working copy.

Unless otherwise indicated, each assignment is due on Friday at 11:59pm of the week in which it is listed.

This schedule is subject to change.

In Project 1, you'll implement nondeterministic finite automata (NFAs). Nondeterminism (essentially, unbounded parallelism) is one of the core concepts in the course, and implementing it will demonstrate how to simulate nondeterminism on deterministic hardware.

In Project 2, you'll write a parser for regular expressions and combine it with NFAs to build a regular expression matcher like grep. Your implementation will be asymptotically much faster than an implementation that uses Perl or Python's built-in regular expressions.

In Project 3, you'll use your regular expression engine to implement a fragment of sed. You'll also show how, in principle, any computer program could be compiled into this fragment of sed.

In Project 4, you'll extend your regular expression matcher to handle backreferences. You'll show how this extended matcher can be used to (slowly) solve the Boolean satisfiability problem and therefore any problem in NP.

Students are expected to attend all classes. Foreseeable unexcused absences should be discussed with the instructor ahead of time.

For excused absences (e.g., documented illness, travel for athletics, job interview), coursework submissions will be accepted late by the same number of days as the excused absence.

Otherwise, you may submit some problems on time for full credit, and other problems late for a penalty. No problem can be submitted more than once. The late penalty increases by 10% per day and stops increasing when it reaches 50%; thereafter, it remains at 50% until the final exam date, after which no work may be submitted.

All course materials written by the instructor and published on this website are licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License, which prohibits reuse for commercial purposes.

All course materials written by the instructor and distributed privately (including through Sakai) should not be redistributed in any way; doing so is a violation of both US copyright law and the University of Notre Dame Honor Code.

Students in this course are expected to abide by the Academic Code of Honor Pledge: “As a member of the Notre Dame community, I will not participate in or tolerate academic dishonesty.”

The following table summarizes how you may work with other students and use printed/online sources:

If an instructor sees behavior that is, in his judgement, academically dishonest, he is required to file either an Honor Code Violation Report or a formal report to the College of Engineering Honesty Committee.

Any student who has a documented disability and is registered with Disability Services should speak with the professor as soon as possible regarding accommodations. Students who are not registered should contact the Office of Disability Services.