CSE 6321 - Solutions to Problem Set 3
1. (7.13) A permutation on the set cfw_1, ., k is a one-to-one, onto function on this set. When p is a
permutation, pt means the composition of p with itself t times. Let
P ERM P OW ER = cfw_< p, q, t > |p = q t where
CSE 6321 - Solution for Problem Set 4
1. (7.26) Let be a 3cnf-formula. An =-assignment to the variables of is one where each clause
contains two literals with unequal truth values. In other words, an =-assignment satises without
assigning three true liter
CSE 6321 - Solutions to Problem Set 5
1. 7.46 Say that two Boolean formulas are equivalent if they have the same set of variables and are true
on the same set of assignments to those variables (i.e., describe the same Boolean function). A Boolean
formula
CSE 6321 - Solutions to Problem Set 1
1. Give an implementation-level description and a formal description (i.e.including the state diagram of the
transition function) of a TM that recognizes
cfw_u#v : u, v cfw_0, 1 and u is v reversed
(1)
Solution:
M = O
CSE 6321 - Solutions to Problem Set 2
1. Prove that the union of countably many countable sets is countable.
Solution:
Let S = cfw_Si iN be a countable family of countable sets, i.e. for each i, we can write Si = cfw_Si,j jN . It
suces to demonstrate a bi
CSE 6321 - Solutions to Problem Set 6
1. An undirected graph is bipartite if its nodes may be divided into two sets so that all edges go from a node
in one set to a node in the other set. Show that a graph is bipartite i it does not contain a cycle that h