CMPS 132 Handout #1
David Helmbold
January 2, 2006
Course Information
Welcome to CMPS 132, Computability and Complexity. The course meets TuTh from 4:00 to 5:45 in
Baskin Engineering 372.
My oce is in the E2 building, room 345b. I can be reached by e-mail

CMP 132 Homework 4 (modied)
To be done in groups of 2. Please work with dierent partners than in the other assignments
6 problems, 23 pts, due Thursday February 16
1. (4 pts) Prove that whenever language L is Turing recognizable, but not
decidable then an

CMP 132 Homework 2
To be done in groups of 2. Please work with dierent partners than in the rst assignment
3 problems, 15 pts, due Thursday January 26.
1. (5 pts) Consider watching a (deterministic, 1-tape) TM running on an
input string, and at each step

COMPUTABILITY
HOMEWORK 4
KRISHNA M. ROSKIN, EMILY A. SCHULTZ, AND RYAN A. BEEBE
Denition 1. We will use the following denitions,
RE: the recursively enumerable languages over an implicitly given alphabet
TM: the set of Turing Machines
S: the complement of

COMPUTABILITY
HOMEWORK 3 (SLIGHTLY CORRECTED BY DPH)
KRISHNA ROSKIN AND ROBERT B. GRAMACY
1. Problem (10.3)
Theorem 1. Suppose that L is recursively enumerable but not recursive, then any
TM accepting L must loop forever on innitely many inputs.
Proof. Si

CMP 132 Handout #4
David Helmbold
January 29, 2001
Comments on Homework 3
1.
(5 pts) Show that if L is recursively enumerable but not recursive then
any TM accepting L must run forever (without crashing) on innitely
many inputs (also 10.3 on page 307).
Ke

CMP 132 Handout #5
David Helmbold
February 5, 2001
Comments on Homework 4
The big ideas and common problems
1.
(5 pts) problem 10.5 (If a nite set of recursively enumerable languages
partition , then the languages are recursive).
Everyone got this one the

Suzanne R Garcia
Robert B. Gramacy
Krishna Roskin
Ryan J. Weber
CMPS 132, Computability
March 7, 2001
Homework 6 Solutions
1. 12.6: (4 pts) Fermats Last Theorem, until recently one of the most famous unproved
statements in mathematics, asserts that there

Homework 2 Solutions
Thanks to: Bobby Gramacy, Suzanne Garcia, Ryan Weber
1. (10 pts) Turing Machine T with reset instead of left.
Assume that at some stage in the computation of T the tape contents are y1z where
cfw_0, 1, and y, z cfw_0, 1, , and the

Suzanne R Garcia
Kelley Nielsen
CMPS 132, Computability
March 7, 2001
Homework 7 Solutions
1. 12.21: (5 pts) Show that the special case of PCP in which the alphabet has only two
symbols is still unsolvable.
Let PCP2 represent the special case of PCP in wh

CMP 132 Handout #2
David Helmbold
January 22, 2001
Comments on Homework 2
1.
(10 pts) In this problem we consider a modied TM model where the
allowable moves are cfw_R, S, G where G means go to the rst tape cell
(this was called reset in class). In class

CMPS 132 Final Review Sheet, W06
The nal exam will be comprehensive, although material after the midterm will be emphasized.
You may have one 3x5 card of handwritten notes, but it will otherwise be a closed-book exam.
The format and style of questions wil

CMPS 132 Handout #1
David Helmbold
January 3, 2001
Course Information
Welcome to CMPS 132, Computability and Complexity. The course meets MW (but not Fridays) in BE
165 from 5:00 to 6:45. My oce is 319 Applied Sciences, I will try to be available after ea

CMPS 132 Midterm review sheet, W06
The material from the midterm will cover chapters 3, 4, and sections 5.1 (except for the section on
reductions via computation histories) and 5.3 as well as things emphasized in lecture.
The topics include:
1. Decision p

CMP 132 Handout #David Helmbold
March 12, 2001
Comments on Homework 8
Note that these are comments on the classs solutions, and not intended
to be sample solutions.
1.
(5 pts) Problem 14.14 on page 411. (Show that if L can be recognized
by a multi-tape TM