# CS 341: Foundations of Computer Science II elearning Section Syllabus, Spring 2015

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1 CS 341: Foundations of Computer Science II elearning Section Syllabus, Spring 2015 Course Info Instructor: Prof. Marvin K. Nakayama Office: GITC 4312 Phone: (Be sure to include CS341EL in the subject line) Only send s about personal matters (e.g., your performance in the class). Post any general questions on moodle (described below). Office Hours: Wednesday, Thursday, 1:00pm 2:00pm, or by appointment. Course Webpage: marvin/cs341 Description This course presents some of the most fundamental results in theoretical Computer Science. These results attempt to answer, in a precise mathematical sense, the following two questions, which are of practical as well as philosophical interest: 1. Can a given problem be solved by computation? 2. How efficiently can a given problem be solved by computation? We focus on problems rather than on specific algorithms for solving problems. To answer both questions mathematically, we will need to formalize the notion of computer or machine. The course outline breaks naturally into three parts: 1. Models of computation (Automata Theory) Finite automata Push-down automata Turing machines 2. What can we compute? (Computability Theory) 3. How efficiently can we compute? (Complexity Theory) Specifically, the topics covered will include regular languages (finite automata, regular expressions), nonregular languages, context-free languages (context-free grammars, pushdown automata), non-context-free languages, Turing machines and variants, Church-Turing Thesis, undecidability, reducibility, time complexity, and complexity classes P, NP, and NP-complete. 1

2 Student Course Outcomes The student course outcomes of the course are to Understand the capabilities and limitations of different models of computation. Understand what problems can be solved by computation and which cannot. Understand what problems can be solved efficiently and those for which there is no known efficient solution. The specific learning objectives are that after completing the course, students will be able to Classify a particular language as regular, context-free, decidable, Turing-recognizable or non- Turing-recognizable. Provide a finite automaton and regular expression for a regular language. Prove that a nonregular language is not regular. Provide a context-free grammar and pushdown automaton for a context-free language. Prove that a non-context-free language is not context-free. Provide a description of a Turing machine for a decidable language. Prove or disprove closure properties (under union, intersection, complementation, Kleene star) of classes of languages. Prove that certain languages are undecidable or non-turing-recognizable. Understand nondeterminism and its role in computation and complexity theory. Understand the significance of complexity classes P, NP and NP-complete, and carry out some NP-completeness reductions. Textbook Michael Sipser, Introduction to the Theory of Computation, Third Edition. Course Technology, 2012, ISBN-10: X, ISBN-13: We will cover Chapters 0 5, and 7, following the schedule given at the end of this handout. The earlier editions of the Sipser book are also acceptable for this class, although the page numbers and sections of the book referenced in the notes and assignments may differ. Prerequisites Before taking CS 341, you must complete all of the following with grades of C or better: 1. A 100-series general undergraduate required course in CS 2. CS 241 (Foundations of Computer Science I) 3. CS 280 (Programming Language Concepts). 2

6 Academic Integrity Students must obey the University Code on Academic Integrity, which you can access from Any student caught violating this will be reported immediately to the Dean of Students. Cheating includes, but is not limited to, communicating with others during exams using unauthorized materials during exams copying/giving a computer program from/to another person. Semester Schedule Unless I announce otherwise, the schedule for the semester is as below. Although you do not need to turn in the homework, you should complete the assignments according to the schedule below. The reading assignments are from the course textbook. Week Topic Modules Reading Homework Complete By 1 Intro, Languages 0, 0a to 0f Chapter 0 HW 1 1/27 2 Regular Languages, DFA 0g to 1c Chapter 1 HW 2 2/3 3 NFA, Reg Exp, Kleene s Thm 1d to 1i Chapter 1 HW 3 2/10 4 Nonregular Lang, CFL 1j to 2a Chapter 1, 2 HW 4 2/17 5 CFG, PDA 2b to 2g Chapter 2 HW 5 2/24 6 Non-CFL, Turing Machines 2h to 3c Chapter 2, 3 HW 6 3/3 7 Church-Turing Thesis 3d to 3i Chapter 3 HW 7 3/10 8 Decidability 4a to 4e Chapter 4 HW 8 3/24 9 Halting Problem, Reductions 4f to 5c Chapter 4, 5 HW 9 3/31 10 Undecidable Problems, Big-O 5d to 5f, 7a, 7b Chapter 5, 7 HW 10 4/7 11 Time Complexity, Class P 7c to 7h Chapter 7 HW 11 4/14 12 Classes P and NP 7i to 7m Chapter 7 HW 12 4/21 13 Class NP-Complete 7n to 7r Chapter 7 HW 13 4/28 14 Review Review1 to 6 5/5 Important Dates The dates/times of exams and assignments are as below, subject to change. 2/3: HW EL due 2/17, 1:00pm NJ local time: Project 1 due Saturday, March 7, 2015: Midterm (tentatively 9:30am - noon) 3/24, 1:00pm NJ local time: Project 2 due 4/21, 1:00pm NJ local time: Project 3 due Saturday, May 9, 2014: Final Exam (tentatively 9:30am - noon) 6

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