CS 336

Sample Questions for Test 2

November 29, 2000

1. Construct pre- and post-condition assertions for the following program, using the Hoare rules.

{ P > 0 }

CONTINUE := true

( while CONTINUE do

Q := 2

LEAVE := false

( while not LEAVE do

K := 1;

( while K * Q <= P do

if K*Q = P then LEAVE = true else skip;

K := K + 1;

)

Q := Q + 1;

if LEAVE then skip else CONTINUE := FALSE;

)

}

Q := Q - 1;

2. Let T be the complete partial order consisting of a, b, c where c is the lower bound of both a and b and neither a nor b is a lower bound of the other.

Construct T x T x T.

3. Let S = { a, b, c }. Let f and g be functions f:SxS->S and g:S -> S. Let E be the set of all legal function calls.

Define a Godel numbering system for E and show how to compute the Godel number of

g(f(a,b))

4. (a) Write an algorithm in pseudo code for checking whether a number N is in the set of prime numbers.

(b) Write an algorithm in pseudo code for deciding whether a number N is in the set of prime numbers.

5. Let P be a checker for set S and let Q be a checker for set Z\S (where Z is the set of natural numbers and S is a subset of Z). Write an algorithm for deciding whether N is a member of S.