1. Do Exercise 5.1
2. Do Exercise 5.2
3. Do Exercise 5.4. Here is a paraphrase of the problem statement.
Conjecture. If A ≤m B and B is a regular language, then A is a regular language.Either give a proof showing the conjecture is true, or give a counterexample showing it is false, i.e., give a non-regular language A, a regular language B, and a mapping reduction from A to B.
4. Do Problem 5.9
5.
Do Problem 7.35.
Use these definitions of DOMINATING-SET
and VERTEX-COVER.
DOMINATING-SET = { <G, k> : undirected graph G has a dominating set of size ≤ k }
and
VERTEX-COVER = { <G, k> : undirected graph G has a vertex cover of size ≤ k }.
6.
SET-PACKING is the following language:
SET-PACKING = { <C, k> : C is a collection of finite sets and C contains ≥ k disjoint sets }
Choose an NP-complete language you know and show that it is mapping reducible to SET-PACKING
in polynomial time.