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CSC 333 (001) Spring 2016 Automata, Grammars, and Computability
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CSC 333 Homework Assignment 1
Out: January 24, 2017
Due: January 30, 2017
Unity ID: MISSING
Using the alphabet = cfw_0, 1, construct two deterministic finite automata.
Machine M 1 should accept every nonempty string that contains at least two and no more
CSC 333 Homework Assignment 2 Sample Solutions
Out: January 30, 2017
Due: February 6, 2017
Unity ID: jdoyle2
1. [25 points] Present both the automaton diagram and the full formal specification hQ, , , S, F i for a nondeterministic finite automaton over th
CSC 333 Homework Assignment 5 Sample Solutions
Out: February 22, 2017
Out: March 1, 2017
Unity ID: jdoyle2
This assignment constructs a regular expression that describes the language accepted by the DFA M over the
alphabet cfw_a, b given by the diagram
b
CSC 333 Homework Assignment 5
Out: February 22, 2017
Out: March 1, 2017
Unity ID: MISSING
This assignment constructs a regular expression that describes the language accepted by the DFA M over the
alphabet cfw_a, b given by the diagram
b
a
b
1
2
a
1. [20
CSC 333 Homework Assignment 1 Sample Solutions
Out: January 24, 2017
Due: January 30, 2017
Unity ID: jdoyle2
Using the alphabet = cfw_0, 1, construct two deterministic finite automata.
Machine M 1 should accept every nonempty string that contains at leas
CSC 333 Homework Assignment 7
Out: March 21, 2017
Due: March 29, 2017
Unity ID: MISSING
This assignment is to convert the context-free grammar G = hV, T, P, Si, where
V
=
cfw_S, A
T
=
cfw_0, 1
S
=
P
=
S
S
A
0S0 | A
1A1 | | 0S
into a Chomsky normal form
IS Decision using Clique Oracle
First, find the size of the maximum indepdent set using the following algorithm.
Algorithm 1: Max IS size
input : G = (V, E)
input : D - Clique oracle function
output: k - Maximum IS size in G
1
2
3
4
5
6
7
k0
be the compl
CSC 333
Spring 2017
Automata, Grammars, and Computability
CSC 333 Spring 2017
Jon Doyle
Department of Computer Science
North Carolina State University
January 23, 2017
NC State University
1 / 368
Automata, Grammars, and Computability
c 2017 by Jon Doyle
C
CSC 333 Homework Assignment 3
Out: February 6, 2017
Out: February 13, 2017
Unity ID: MISSING
1. [25 points] Consider the eNFA M over = cfw_0, 1 with the state diagram
1
0
2
3
1
6
1
1
4
5
Give a table indicating the -closure of each of the states in M .
2.
CSC 333 Homework Assignment 4
Out: February 16, 2017
Out: February 22, 2017
Unity ID: MISSING
Let = cfw_0, 1, and consider the language
L = cfw_0n 1u0n | n 1, u
The following problems relate to showing that L is not regular by using the Pumping Lemma.
As
Part II CPU Scheduling (45 points)
True/False (10 points)
_F_ FCFS scheduling is preemptive scheduling.
_T _ Rate Monotonic Scheduling is a priority-scheduling algorithm.
_T _ Aging is a technique of gradually increasing the priority of processes that wai
CSC 333 Homework Assignment 6 Sample Solutions
(corrected)
Out: March 13, 2017
Due: March 20, 2017
Unity ID: jdoyle2
This corrected set of sample solutions corrects three errors in the original version. The amended
solution to Problem 2 corrects a mislead
CSC 333 Homework Assignment 4 Sample Solutions
(Corrected)
Out: February 16, 2017
Out: February 22, 2017
Unity ID: jdoyle2
Let = cfw_0, 1, and consider the language
L = cfw_0n 1u0n | n 1, u
The following problems relate to showing that L is not regular b
CSC 333 Homework Assignment 3 Sample Solutions
(Corrected)
Out: February 6, 2017
Out: February 13, 2017
Unity ID: jdoyle2
1. [25 points] Consider the eNFA M over = cfw_0, 1 with the state diagram
1
0
2
3
1
6
1
1
4
5
Give a table indicating the -closure of
CSC 333 Homework Assignment 6
Out: March 13, 2017
Due: March 20, 2017
Unity ID: MISSING
Let L be the language over the alphabet cfw_x, y consisting of those strings in which there are exactly as many ys as
xs. The empty word is in L, as are xy and yxyx, b
CSC 333 Homework Assignment 2
Out: January 30, 2017
Due: February 6, 2017
Unity ID: MISSING
1. [25 points] Present both the automaton diagram and the full formal specification hQ, , , S, F i for a nondeterministic finite automaton over the alphabet = cfw_
CSC 333
Spring 2017
Automata, Grammars, and Computability
CSC 333 Spring 2017
Jon Doyle
Department of Computer Science
North Carolina State University
January 23, 2017
NC State University
1 / 368
Automata, Grammars, and Computability
c 2017 by Jon Doyle
C
CSC 333, Spring 2017
Nonregular Languages
Identifying them with the Pumping Lemma
Jon Doyle
Instructor
Regular Languages Recognized by FA, L(M)
Definition: Language L(M) is regular if there is a finite automata M:
Finite Automata
Push Down Automata
Regula
CSC 333, Fall 2016
Homework 2
page 1 of 2
Due Sunday, September 4 at 11:45 PM
Total points = 13
In all problems calling for design of a DFA, you must document, for each state q, the set L(q), i.e.,
the set of strings that will lead to q. If you dont do th
CSC 333, Fall 2016
Homework 1
page 1 of 1
Due Sunday, August 28 at 11:45 PM
Total points = 36
Please submit homework solutions electronically using the WolfWare submit mechanism at
https:/courses.ncsu.edu/csc333/
Your submissions should be pdf files gener
CSC 333 Homework Assignment 10 Sample
Solution
Due 11/25/2013 before class
November 13, 2013
Please typeset your answers.
1. [40 points] Prove that the language L1 L2 , where L1 is recursively enumerable and L2 is recursive, is recursively enumerable. You
CSC 333 Homework Assignment 9 Sample
Solution
Due 11/8/13 before class
October 29, 2013
Please typeset your answers.
1. Construct a deciding TM for the language described by the regular expression (0 + 1) that, when read left to right, give a binary repre
CSC 333 Homework Assignment 8 Sample
Solution (Corrected)
Due 10/30/2013 before class
October 17, 2013
Please typeset your answers.
1. [50 points] Construct a pushdown automaton for the language
L = cfw_03n 12n | n 1.
A:
2
0,
3
0,
0, X
0
, $
1
,
4
,
8
CSC 333 Homework Assignment 7 Sample
Solution
Due 10/25/2013 before class
October 17, 2013
Please typeset your answers.
1. Let = cfw_0, 1. In this problem, we will prove that the language
L = cfw_0k 1u0k | k 1, u
is not regular by using the Pumping Lemma
CSC 333 Homework Assignment 6 Sample
Solution
Due September 30, 2013 before class
September 20, 2013
Please begin the solution to each problem on a separate page. The
LaTeX command \newpage starts a new page. Drawing automata diagrams is
simplied by use o
CSC 333 Homework Assignment 4
Due 9/9/2013
August 30, 2013
Please begin the solution to each problem on a separate page.
The LaTeX command \newpage starts a new page.
Please typeset your answers.
1. Prove that the following function f : Z N is a bijection
CSC 333, Fall 2016
Homework 3
page 1 of 1
Due Sunday, September 11 at 11:45 PM
Total points = 14
In all problems calling for design of an automaton (DFA or NFA), you must document, for each
state q, the set L(q), i.e., the set of strings that will lead to