Other Math Answers

To completely write the program in FORTRAN and rewrite the 1% code in assembly language, if the project needs 13 days, the team consists of

a) 13 programmers
b) 10 programmers
c) 8 programmers
d) 100/13 programmers

If the strings of a language L can be effectively enumerated in
lexicographic (i.e. alphabetic) order, which of the following statements
is true?
(A) L is necessarily finite
(B) L is regular but not necessarily finite
(C) L is context free but not necessarily regular
(D) L is recursive but not necessarily context free

Nobody knows yet if P = NP. Consider the language L defined as
follows

L=(0 + 1)* if P=NP
L= φ otherwise

Which of the following statements is true?
(A) L is recursive
(B) L is recursively enumerable but not recursive
(C) L is not recursively enumerable
(D) Whether L is recursive or not will be known after we find out if P = NP

Given an arbitrary non-deterministic finite automaton (NFA) with N states, the maximum number of states in an equivalent minimized DFA is least

a) N^2
b) 2^N
c) 2N
d) N!

the logic of pumping lemma is a good example of
a)the pigeonhole principle
b)the divide and conquer technique
c)recursion
d)iteration

A one-dimensional cellular automaton is seeded (initialized) with the following values at time t0.
....00001010000....
The automaton evolves according to the rule 01010110. What will the automaton look like at time t3?

a) ...00101001100....
b) ...11001000110....
c) ...10101001001....
d) ...01101110110....
e) ...00011011000....

Given the following rule for the evolution of a cellular automation (a - 1'a1') + (a0 a1'). Which of the following is the binary number representation of the rule?

a) 01001010
b) 00101100
c) 00010000
d) 11001110
e) 01000101

There are two strain of flu(F) virus and two types of vaccine. The first vaccine(V1), is 0.85 effective against F1 and 0.70 effective against F2, while the second vaccine(V2) is 0.60 effective against F1 and 0.90 against F2. The public health service is player 1 and nature is player 2. The service has to decide what percentage of vaccines manufactured and made available to the public are of V1 and V2. Determine how the public health service should proceed.

Please apply the gradient form of the Karush-Kuhn-Tucker (KKT) theorem to minimize the function f(x,y) = (x+1)^2 + y^2 over all x>=0, y>=0.

Matrix Games:

If we are given an arbitrary I by J matrix A, there exists a greater than 0 so that the matrix B with entries Bij = Aij + a has only positive entries. Show that any optimal randomized probability vectors for the game with pay-off matrix B are also optimal for the game with pay-off matrix A.