CS 172, Spring 1999
Midterm Exam 2
Manual Blum
This is a CLOSED BOOK examination.• Calculators ARE permitted.• Do all your work on the pages of this examination.• For most problems, you may answer YES, NO, "I think so", "I think not", or "I don't know".• Give reasons -- carefully written correct reasons -- for your YES/NO answers, and to the extent you
can for your "I think such and such" answers.
•
This examination has 7 problems, worth a total of 97 points.•
Problem #1
(1 pt)
a) The product of binary numbers 1011 and 1101 is
1011* 1101 = _______________________________________.
(10 pts: 1 pt each; double this if all are correct)
b) In spaces to the right, write YES or NO (or "I think so" or "I think not" or "I don't know").
The length (in bits) of the product of an m-bit number and an n-bit number, for positive integers m and n, is:
O(mn) bits_____• O(m+n) bits_____• m+n+O(1) bits _____• MAX{m,n} bits _____• min{m,n} bits _____•
Define the Computational Decision Problem ZMP as follows:
DECISION PROBLEM ZMP (Zeroes of a Multivariate Polynomial)
INSTANCE:
A multivariate polynomial* with interger coefficients.• All coefficients given in binary.• All degrees given in unary or binary, depending.•
QUESTION: Does the given polynomial have a root over {0,1}?
EXAMPLE: The same f as it appears with unary and binary degress
Unary degrees: f(x,y,z) = (1+x)^11 + (y^1111)*(1+z^111111) - 3
Binary degrees: f(x,y,z) = (1+x)^2 + (y^4)*(1+z^6)-3
CS172, Midterm 2, Spring 1999
CS 172, Spring 1999 Midterm Exam 2 Manual Blum 1
