Syllabus:
Fall 2009
Instructor:
Professor Sudkamp
Time:
4:10—5:50 Tuesday, Thursday
Room:
161 Rike
Office
Hours: 3:00-4:00 Tuesday, Thursday, and by appointment
Office:
303 Russ Engineering Center
Email:
tsudkamp@cs.wright.edu
Phone:
775-5118
This course is an introduction to one of the fundamental topics in the theory of computer science: computability theory. Computability theory is concerned with determining whether there is an algorithmic solution to a problem. The study of computability uses the Turing machine as the basic computational model. A Turing machine is a random access, read-write, finite state automaton. Although the Turing machine provides a simple computational framework, the Church-Turing thesis asserts that any problem that can be solved in any algorithmic manner can be solved by a Turing machine.
The
text for the course is the third edition of Languages
and Machines: An Introduction to the Theory of Computer Science. Some
material from CS 466/666 and discrete mathematics is a prerequisite for this
course. It is assumed that students are
familiar with finite state machines, inductive proofs, regular expressions, and
derivation of strings using the rules of a grammar. The background material may be reviewed in
chapters 1, 2, 3, and 5 of the text.
Topics: The topics to be covered in this course include
·
Review of naive set theory with emphasis on cardinality, diagonalization, and proofs of nonexistence using
self-reference. Countable and
uncountable sets. Sections 1.1-1.3.
·
Turing machines as language acceptors.
Deterministic and nondeterministic machines. Multi-track and multi-tape machines. Turing
machines as enumerators. Chapter 9.
·
Decision problems. Problem
reduction. Church-Turing thesis.
Universal Turing machines. Chapter 11.
·
Undecidability: The Halting Problem and other undecidable problems of algorithmic computation. The Post correspondence problem. Rice's theorem. Chapter 12.
·
Functional characterization of computability. Recursive and mu-recursive
functions. Chapters 13.
Grades
will be assigned using the following scale:
A - 90% or above
B - 80% - 89%
C - 70% - 79%
D - 60% - 69%
F - below 60%
I
reserve the right to adjust (lower) the scale to utilize gaps in the
distribution, but this will be done minimally if at all.
The
exams for graduate students will contain more problems than the undergraduate
exam. These additional problems will be
more theoretic in nature, reflecting the added sophistication expected of
graduate students. They will also cover
material in the readings that may not be represented in any of the assigned
homework.
All
exams are open book (no notes): it is not the objective of this course to be an
exercise in memorization. However, over
reliance on the book is a sure-fire way to do poorly on an exam. Know the material before and use the book
only as a safety net.
There
are no makeup exams except for documented emergencies. Examples of acceptable
documentation are a letter from a doctor (on his/her letterhead) indicating
that you were unable to take the exam due to illness or a letter from an
employer indicating that you will be out of town on company business at the
scheduled exam time. A missed exam
counts as a 0 and may be dropped as the lowest score.
Exam Dates:
Thursday, September 17
Thursday, October 1
Thursday, October 15
Thursday, October 29
Tuesday, November 18 5:45-7:45 pm
There
will be homework, both reading and exercises, assigned at each class. The
homework will not be collected, but is assigned to increase your understanding
of the topics and to help you prepare for the exams. Time will be taken in each class period to
discuss homework assigned in the previous class. I urge you to work together on the homework
problems. This makes the entire process
more enjoyable and fruitful. Sharing
your ideas and listening to those of others will increase your understanding
and facilitate the solution of the problem.
Office Hours: My office hours for the fall
quarter are given on the first page of this syllabus. For students who are not free at these times,
see me, email me, or call me and we will arrange a time that is convenient for
you. My office is 303 Russ Engineering.
For
general questions, you may reach me by email at tsudkamp@cs.wright.edu or call
775-5118. The e-mail and telephone are
for procedural questions such as "when is the exam?" or "what
will be covered?" or "what did I miss in the last class when I was
kept away by the hurricane?" For
answers to homework, exam problems, or help on course topics see me in person.
Attendance: Attendance at classes is
strongly recommended. If you miss a
class, it is your responsibility to obtain class notes from other students to
be prepared for subsequent topics. As noted earlier, there will be no make-up
exams except for documented emergencies.