Formal Languages and Automata

Spring 2018

(198:452 & 198:508)

 

Course Info

Instructor: Swastik Kopparty (swastik.kopparty@gmail.com)

Class Time and Place: Tuesdays and Thursdays 3:20pm – 4:40pm, in TIL 116 (Tillett Hall, Livingston Campus).

Office Hours:  Thursday 11 am-12 noon (Hill 432)

Textbook: Introduction to the Theory of Computation, by Sipser, Third Edition

TA: Aditi Dudeja (ad1222@rutgers.edu)

TA Office Hours: Tuesday 10am-11am, Friday 10am-11am (Hill 202)

 

There will be HW every 1-1.5 weeks.

Grading: HW 35%, Midterm 1: 30%, Midterm 2: 30%, Participation: 5%

 

Homework

·       Homework 0 (finish by Jan 18) (Click here for CHAPTER 0)

o   Read Chapter 0. Look up whatever you need to in order to understand it. If you can’t understand Chapter 0, this course will be too difficult for you.

o   Solve the following problems from Chapter 0 and check your answers with some random classmates

§  0.1, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.10, 0.12, and (slightly tricky) 0.13

o   Do not turn anything in.

·       Homework 1 (NOW DUE Tuesday, Jan 30 in class)

o   Problems from the book:

§  1.6.a, 1.6.b, 1.6.g, 1.6.i, 1.7.e, 1.8.a, 1.9.a, 1.10.a, 1.31,  1.34, 1.41

·       Homework 2 (Due Tuesday, Feb 6 in class)

o   Problems from the book:

§  1.16b, 1.17a, 1.20e, 1.21b, 1.29b, 1.37, 1.43, 1.70, 1.71

·       Homework 3 (Due Tuesday, Feb 13 in class)

o   Problems from the book:

§  2.1, 2.4c, 2.4e, 2.9, 2.10, 2.6b, 2.13, 2.14, 2.16, 2.26, 2.30a, 2.31

·       Homework 4 (Due Thursday, March 1 in class)

o   Problems from the book:

§  3.6, 3.8b, 3.11, 3.15b, 3.15e, 3.16b, 3.16d, 3.18, 4.5, 4.7, 4.8, 4.18, 4.20

·       Homework 5 (Due Thursday, April 12 in class)

o   Problems from the book:

§  6.14, 6.19, 7.5, 7.6, 7.7, 7.13, 7.14, 7.9, 7.17, 7.18, 7.20, 7.22, 7.34, 7.35, 7.39

§  bonus problems (for extra credit): 6.16, 7.26, 7.27, 7.28, 7.29, 7.30, 7.31

 

 

Lecture Schedule

·       January 16: course overview, finite automata, regular languages

·       January 18: nondeterministic finite automata

·       January 23: NFAs and regular operations

·       January 25: regular expressions, the pumping lemma

·       January 30: applications of the pumping lemma

·       February 1: context free grammars (notes for CYK parsing algorithm – from Hopcroft-Motwani,-Ullman)

·       February 6: push down automata

·       February 8: pumping lemma for context free languages

·       February 13: Turing machines, Church-Turing thesis

·       February 15: universal Turing machine, countability, existence of non-Turing-recognizable sets

·       February 20: undecidability via diagonalization

·       February 22: undecidability (and non-Turing-recognizability) via reductions

·       February 27: MIDTERM 1

·       March 1: oracles, Turing reductions

·       March 6: compression, Kolmogorov complexity

·       March 8: Kolmogorov complexity (continued)

·       March 13: NO CLASS

·       March 15: NO CLASS

·       March 20: time complexity, space complexity

·       March 22: the time hierarchy theorem, NP

·       March 27: some problems in NP

·       March 29: NP completeness

·       April 3: NP completeness

·       April 5: NP completeness

·       April 10: MIDTERM 2

·       April 12:

·       April 17:

·       April 19:

·       April 24:

·       April 26: