CSE 105: Automata and Computability Theory
Winter 2015
Homework #2
Due: Friday, January 23th, 2015, 11:59 pm
Problem 1 (Automata Tutor) Complete the problems that constitute CSE 105s HW2
on Automata Tutor. (Problems will be posted soon.)
Problem 2 (Closur
CSE 105: Automata and Computability Theory
Autumn 2012
Problem Set #1
Due: Monday, October 15th, 2012
Problem 1 Warmup.
a. Prove that if a language L contains nitely many elements then it is regular.
b. If a language L contains innitely many elements, can
CSE 105: Introduction to the Theory of Comptuation
Spring 2012
Solution Set 2
Instructor: Alexander Tsiatas
Due on: Tue. April 17, 2012
Problem 1
In JFLAP, draw an NFA for the following language: cfw_w  w has only alternating as and bs . Whether you
thin
CSE 105: Introduction to the Theory of Comptuation
Spring 2012
Solution Set 1
Instructor: Alexander Tsiatas
Due on: Wed. April 11, 2012
Problem 1
There are many possibilities here. This is just one example.
(a) Suppose you want a DFA that accepts strings
CSE 105: Automata and Computability Theory
Winter 2011
Homework #2
Due: Thursday, January 20th, 2011
a,b
a,b
1
2
a,b
3
4
a
Figure 1: Machine M1 .
Problem 1 Convert the NFA M1 , given in Figure 1, into an equivalent DFA, using the
NFADFA transformation al
CSE 105

HOMEWORK
1 SOLUTIONS
prepared by Lawrence Cayton
0.1
a. Odd natural numbers b. Even integers c. Even natural numbers d. Even natural numbers that are multiples of 3 e. Symmetric binary numbers f. The empty set
0.2
a. {1, 10, 100} b.
CSE 105: Introduction to the Theory of Comptuation
Fall 2010
Problem Set 5
Instructor: Daniele Micciancio Due on: Wed. Nov 10, 2010
Problem 1
Let BIGGER be the set of all strings over the alphabet cfw_0, 1, > of the form x > y , where x and y are binary n
CSE105 (Winter 2014): Homework 4 Solution
Instructor: Daniele Micciancio
Due on Wednesday, February 12, 2014, in class.
1
Pumping Lemma
Suppose for the sake of contradiction that L : x + y = z where x, y, z cfw_0, 1 were indeed regular. The
pumping lemma
CSE 105: Automata and Computability Theory
Winter 2011
Homework #3
Due: Tuesday, February 1st, 2011
Problem 1 Pumping Lemma practice. For each of the following languages, and for a pumping length p, give a string w that can be used to establish that the l
CSE 105 HW#1
Problem Solving
1)
(a) In this simple task, we want to end with the string ass.
(b)
(c)
1. Q = cfw_q0, q1, q2, q3
2. = cfw_a, s
3. is described as
q0
q1
q2
q3
a
q1
q1
q1
q1
4. q0 is the start state
5. F = cfw_q3
2)
(a) cfw_w  w starts with 0
CSE105 (Winter 2014): Homework 3
Instructor: Daniele Micciancio
Due on Wednesday, February 5, 2014.
Solutions to this homework assignment should consists of both a writeup with the proofs for problems
2, 4 and 5, and a collection of JFLAP les and Haskell
CSE 105 Homework 1
Due January 15
You may (and are encouraged to) discuss the problems with other students, but what you hand in must be your own work. If you do not understand a problem or nd a mistake, please email William at wmatthews@cs.ucsd.edu. In
Theory of Computation  CSE 105
HalfLanguage
Solution for Problem 1.42 Idea: Sine is regular, Let be a DFA recognizing . The idea for recognizing is the following: We are given a string and we need to check if there is a string of equal
CSE 105: Introduction to the Theory of Comptuation
Fall 2010
Problem Set 3
Instructor: Daniele Micciancio Due on: Wed. Oct. 20, 2010
Problem 1
Let L be the set of all strings (over the alphabet cfw_0, 1, +, =) of the form x + y = z , where x, y and z are
CSE105 Homework Number 1 SOLUTIONS
October 6, 2010
Guidelines:
solutions to the homework should be submitted electronically, following the instructions on
the class website. As part of your solutions to this assignment you should submit: 1. A le with the
Homework 2 Solutions
CSE105 Daniele Micciancio Winter 2014
January 31, 2014
Problem 1
(a)
(b)
1
(c)
2
(d)
Problem 2
The steps are excluded for the sake of brevity, but the DFAs you should end up with are as
follows:
(a)
(b) (The edge below labeled with a
CSE 105: Automata and Computability Theory
Winter 2011
Homework #5
Due: Tuesday, March 1st, 2011
Problem 1 Let COMPLDFA be the language
A, B
A and B are DFAs over the same alphabet and L(A) = L(B )
.
(Notice the complementation bar over L(B ) above!) Show
CSE 105 HW#8
(1) ATM undecidability. (10pts)
The use of the proof to show ATM is undecidable is as follows. ATM represents a language
that takes in <M,w> where M is a Turing Machine and w is a input that M takes in. Start
with another Turing Machine (an i
CSE 105: Introduction to the Theory of Comptuation
Fall 2010
Problem Set 2
Instructor: Daniele Micciancio Due on: Wed. Oct 13, 2010
Guidelines: Same as for homework 1. Solutions to the homework should be submitted electronically using turnin, and you shou
Theory of
Computation
Theory of Computation Peer Instruction Lecture SlidesbyDr. Cynthia Lee, UCSD are
licensed under aCreative Commons Attribution NonCommercial ShareAlike 3.0 Unported
License.
Based on a work atwww.peerinstruction4cs.org .
1
On beyond
Theory of
Computation
Theory of Computation Peer Instruction Lecture SlidesbyDr. Cynthia Lee, UCSD are
licensed under aCreative Commons Attribution NonCommercial ShareAlike 3.0 Unported
License.
Based on a work atwww.peerinstruction4cs.org .
1
Course Up
Theory of
Computation
Theory of Computation Peer Instruction Lecture SlidesbyDr. Cynthia Lee, UCSD are
licensed under aCreative Commons Attribution NonCommercial ShareAlike 3.0 Unported
License.
Based on a work atwww.peerinstruction4cs.org .
1
Father of
cfw_ 
Module
:
Description
:
Author
:
Stability
:

module DFA where
DFA
Definition of Deterministic Finite Automata
Daniele Micciancio
experimental
 Data type representing a Deterministic Finite Automaton, parametrized by a
type of states.
type DFA s
Theory of Computation Peer Instruction Lecture SlidesbyDr. Cynthia Lee, UCSD are
licensed under aCreative Commons Attribution NonCommercial ShareAlike 3.0 Unported
License.
Based on a work atwww.peerinstruction4cs.org .
THE PUMPING LEMMA
PROVING A LANGU
Theory of
Computation
Theory of Computation Peer Instruction Lecture SlidesbyDr. Cynthia Lee, UCSD are
licensed under aCreative Commons Attribution NonCommercial ShareAlike 3.0 Unported
License.
Based on a work atwww.peerinstruction4cs.org .
1
Extra Cre
Homework 4 Solutions
1. (a) To show that L = cfw_wtwR  w 2 cfw_0, 1 , t 2 cfw_0, 1 is not regular, we will use the
pumping lemma in a proof by contradiction.
Assume (towards contradiction) that L is regular. Let p be the pumping length for L
given by the
Theory of
Computation
Theory of Computation Peer Instruction Lecture SlidesbyDr. Cynthia Lee, UCSD are
licensed under aCreative Commons Attribution NonCommercial ShareAlike 3.0 Unported
License.
Based on a work atwww.peerinstruction4cs.org .
1
On beyond
Theory of
Computation
Theory of Computation Peer Instruction Lecture SlidesbyDr. Cynthia Lee, UCSD are
licensed under aCreative Commons Attribution NonCommercial ShareAlike 3.0 Unported
License.
Based on a work atwww.peerinstruction4cs.org .
1
Continuat
Theory of
Computation
Theory of Computation Peer Instruction Lecture SlidesbyDr. Cynthia Lee, UCSD are
licensed under aCreative Commons Attribution NonCommercial ShareAlike 3.0 Unported
License.
Based on a work atwww.peerinstruction4cs.org .
1
Father of
Theory of
Computation
Theory of Computation Peer Instruction Lecture SlidesbyDr. Cynthia Lee, UCSD are
licensed under aCreative Commons Attribution NonCommercial ShareAlike 3.0 Unported
License.
Based on a work atwww.peerinstruction4cs.org .
1
If a lang
CSE 105
THEORY OF COMPUTATION
Fall 2016
http:/cseweb.ucsd.edu/classes/fa16/cse105abc/
Todays lecture
Reductions, Reductions, Reductions!
Did I say reductions?
More reductions
Reading: Chapter 5
Reduction from A to B
A < B, If B is decidable, then A is de
CSE 105
THEORY OF COMPUTATION
Fall 2016
http:/cseweb.ucsd.edu/classes/fa16/cse105abc/
This Week
Beyond Theory of Computation:
Computational Complexity
Reading: Sipser Chapter 7
Not covered in final exam
Revisit familiar topics
Diagonalization
Reduction
N
CSE 105
THEORY OF COMPUTATION
Fall 2016
http:/cseweb.ucsd.edu/classes/sp16/cse105ab/
Today's learning goals
Summarize key concepts, ideas, themes from CSE 105.
Approach your final exam studying with confidence.
Identify areas to focus on while studyin
CSE 105
THEORY OF COMPUTATION
Fall 2016
http:/cseweb.ucsd.edu/classes/fa16/cse105abc/
This Week
Beyond Theory of Computation:
Computational Complexity
Reading: Sipser Chapter 7
Not covered in final exam
Revisit familiar topics
Diagonalization
Reductions
CSE 105
Homework 7
Due: Tuesday November 29, 2016
Instructions
Homework should be done in groups of one to three people. You are free to change group
members at any time throughout the quarter. Problems should be solved together, not divided
up between pa