CAS 705. Sample solutions to the assignment 1 (many questions have more than one solutions).
Total of this assignment is 149 pts. Each assignment is worth 25%.
1.[6]
Consider a typical vending machine that dispenses a persons choice of candy after it has

CAS 705, Computability and Complexity
Assignment 2
Xiao Shu (0901994)
[email protected]
October 22, 2009
Question 1
For a given graph G = (V, E), we can verify whether S, T V is a cut and whether its size
is no less than k by counting the number of edges c

CAS 705, Computability and Complexity
Assignment 1
Xiao Shu (0901994)
[email protected]
October 10, 2009
n
1. We are going to show the language L = cfw_12 |n 0 being non-regular by using
contradiction. Suppose L is regular. By the Pumping Lemma, for a suci

Assignment 4 Solutions
CAS705 Fall 2005
Due on November 7th
1. For part (a), use essentially the same machine that decides L in time n6 to decide pad(L, n2 ) in time n3 by making it ignore the trailing junk1 (note that |pad(x, |x|2 )| = |x|2 = m, and x is

Assignment 5
Solutions Due on November 24 In class, at the beginning of the lecture
CAS705 Fall 2006
The work you submit must be your own. You may discuss problems with each other; however, you should prepare written solutions alone. In particular, you sh

Assignment 4
Solutions Due on November 10 In class, at the beginning of the lecture
CAS705 Fall 2006
The work you submit must be your own. You may discuss problems with each other; however, you should prepare written solutions alone. In particular, you sh

Assignment 1
Solutions Due on September 29 In class, at the beginning of the lecture
CAS705 Fall 2006
The work you submit must be your own. You may discuss problems with each other; however, you should prepare written solutions alone. In particular, you s

Assignment 2
Solutions Due on October 13 In class, at the beginning of the lecture
CAS705 Fall 2006
The work you submit must be your own. You may discuss problems with each other; however, you should prepare written solutions alone. In particular, you sho

Assignment #4
CAS 705
Computability and Complexity
Jason Jaskolka
0546444
Dr. Michael Soltys
November 24, 2009
CAS 705
Assignment #4
0546444 - Jason Jaskolka
Question 1
Let G be a group, and suppose that we have an algorithm to solve the discrete logarith

CAS 705. Sample solutions to the assignment 1. Total of this assignment is 157pts, but 100% is
150. Each assignment is worth 5% of total.
1.[11] a.[2]
C
a
q1
q0 6 a 6 q1 6 b 6 q2 6 a 6 q0 6 a 6 q1
q0 6 b 6 q0 6 b 6 q0 6 b 6 q0 6 a 6 q1 6 b 6 q2 6 b 6 q2
q

Computability and Complexity
Push-Down Automata
CAS 705
Ryszard Janicki
Department of Computing and Software
McMaster University
Hamilton, Ontario, Canada
[email protected]
Ryszard Janicki
Computability and Complexity
1 / 45
Pushdown Automata (PDAs): A

Computability and Complexity
Rewriting Systems and Chomsky Grammars
CAS 705
Ryszard Janicki
Department of Computing and Software
McMaster University
Hamilton, Ontario, Canada
[email protected]
Ryszard Janicki
Computability and Complexity
1 / 48
Rewritin

Computability and Complexity
Turing Machines
CAS 705
Ryszard Janicki
Department of Computing and Software
McMaster University
Hamilton, Ontario, Canada
[email protected]
Ryszard Janicki
Computability and Complexity
1 / 47
Introduction
It is named after

CAS 705
Assignment #1. Due January 26 (Tuesday), 2016, in class, or in my mailbox before the
office closure, or slip under the door to my office.
The assignment is not difficult, but quite labour consuming. Do not wait until the very last day.
1.
Consider

Computability and Complexity
Complexity and Turing Machines. P vs NP Problem
CAS 705
Ryszard Janicki
Department of Computing and Software
McMaster University
Hamilton, Ontario, Canada
[email protected]
Ryszard Janicki
Computability and Complexity
1 / 79

Computability and Complexity
Decidability, Undecidability and Reducibility;
Codes, Algorithms and Languages
CAS 705
Ryszard Janicki
Department of Computing and Software
McMaster University
Hamilton, Ontario, Canada
[email protected]
Ryszard Janicki
Comp

Computability and Complexity
Non-determinism, Regular Expressions
CAS 705
Ryszard Janicki
Department of Computing and Software
McMaster University
Hamilton, Ontario, Canada
[email protected]
Ryszard Janicki
Computability and Complexity
1 / 49
Non-determ

Computability and Complexity
Model Theory, Decidability of Logical Theories, Gdel Theorems
CAS 705
Ryszard Janicki
Department of Computing and Software
McMaster University
Hamilton, Ontario, Canada
[email protected]
Ryszard Janicki
Computability and Com

Computability and Complexity
Recursive Functions
CAS 705
Ryszard Janicki
Department of Computing and Software
McMaster University
Hamilton, Ontario, Canada
[email protected]
Ryszard Janicki
Computability and Complexity
1 / 18
Introduction
This is a mode

Computability and Complexity
Sequences and Automata
CAS 705
Ryszard Janicki
Department of Computing and Software
McMaster University
Hamilton, Ontario, Canada
[email protected]
Ryszard Janicki
Computability and Complexity
1 / 33
Outline
Languages and Ma

Computability and Complexity
Pumping Lemma, Closures, Fixed-points, Equations, Nerode
Relation, Minimization, Mealy and Moore Machines
CAS 705
Ryszard Janicki
Department of Computing and Software
McMaster University
Hamilton, Ontario, Canada
[email protected]

Assignment #3
CAS 705
Computability and Complexity
Jason Jaskolka
0546444
Dr. Michael Soltys
November 10, 2009
CAS 705
Assignment #3
0546444 - Jason Jaskolka
Question 1
This exercise is related to the Immerman-Szelepcsnyi theorem.
e
Suppose that the membe

CAS 705
Sample solutions to the assignment 3. Total of this assignment is 210 pts. No need to be so
precise as below.
1.[10] a.[5]
b.[5]
x = ax c by c a c g
y = by c az
z = ax c by c a
x = ax c by c a c g
y = by c a(ax c by c a) = by c cax c cby c ca = ca

CAS 705. Sample solutions to the assignment 4. Total of this assignment is 168pts. 100% equals
160pts.
1.[5]
If x Y* y then either x=y or x = w1cw2c.cwk, where wi 0 cfw_a,b,c*, and y was derived by
replacing cs in appropriate way.
Since c Yk z implies z =

Assignment 4 Solutions
CAS705 Fall 2005
Due on November 7th
1. For part (a), use essentially the same machine that decides L in time n6 to decide
pad(L, n2 ) in time n3 by making it ignore the trailing junk1 (note that |pad(x, |x|2 )| =
|x|2 = m, and x is

Assignment 5
CAS705 Fall 2005
Due on November 21th
The work you submit must be your own. You may discuss problems with each other;
however, you should prepare written solutions alone. In particular, you should not leave with
any written notes from such di

Final Exam
Due: December 15
CAS705 Fall 2011
strict deadline
A
You are encouraged to typeset your exam, preferably in L TEX.
1. In Cooks seminal 1975 paper Feasible constructive proofs, where he introduces the now
classical theory PV, he uses a nice resul

Assignment 6
CAS705 Fall 2005
Due on November 30th
The work you submit must be your own. You may discuss problems with each other;
however, you should prepare written solutions alone. In particular, you should not leave with
any written notes from such di

Assignment 4 Due on November 10 In class, at the beginning of the lecture
CAS705 Fall 2006
The work you submit must be your own. You may discuss problems with each other; however, you should prepare written solutions alone. In particular, you should not l

Assignment 2 Due on October 13 In class, at the beginning of the lecture
CAS705 Fall 2006
The work you submit must be your own. You may discuss problems with each other; however, you should prepare written solutions alone. In particular, you should not le