Module 13 Worksheet
In Class Questions
1) (S5) Consider the following two problems. Define what a natural notion of size might
be for these problems.
Shortest path problem
Input: Graph G=(V,E)
2 nodes s and t
Task: Output the shortest path from
node s to node t
Longest path problem
Input: Graph G=(V,E)
2 nodes s and t
Task: Output the longest path from
node s to node t
2) (S6) Which of the following problems belong to Poly?
Let n be the standardized input size. Let the right hand side be the worst-case running
time required to solve an input instance of the given problem of size n.
2(log n) (log n).
n1,000,000.
n7
2n
(log n)5.
3) (S11) How is automata theory similar to complexity theory?
4) (S11) How are they different?
Take home review questions
1) How do we define how hard a problem is to solve?
2) Generally speaking, a problem is “easy to solve” if it belongs to Poly. What does it
mean to be long to Poly?
3) True or false and explain your answer. Automata theory is different from complexity
theory in that Automata theory focuses on the unsolvable problems.