CSI 409 Fall 2014: Homework #1
Some answers and hints
1. State whether the following quantied formulae are true over the natural numbers
N = cfw_1, 2, :
(i) x y z w [xy = w + z]
False: The -player can win by picking x = 1 and z = y + 1. Since w cannot be

CSI 409 Fall 2016: Homework #2
Some answers and hints
1. Exhibit finite, nonempty languages A, B and C such that AC BC, but A 6 B.
A = , a, aa, aaa, aaaa , B = , a, aaa, aaaa , C = , a, aa .
2. Let L1 = a, bb and L2 = , b . Explain why L1 L2

CSI 409 Fall 2016: Homework #1
Some answers and hints
1. State whether the following quantified formulae are true over the natural numbers
N = cfw_1, 2, :
(i) x y z xy2 6= z2
False: The -player can win by picking x = 4 and z = 2y.
(ii) x y z (x = y2 ) (y

CSI 409: DFA design problems
Some answers and hints
1. Disprove the following: A (B C) = (A B) (A C) for all languages A, B, C.
Take A = cfw_, a, B = cfw_, C = cfw_a.
2. Disprove the following: for all languages A, B
A ( B A ( B
Take A = cfw_a and B = cf