1. Do Problem 4.21
2. For this problem, assume it is known that the
language ALLCFG is undecidable.
Do Exercise 5.1 as follows.
First define the language EQCFG using
set notation.
Then prove that
EQCFG
is undecidable
if
ALLCFG
is.
3. Do Exercise 5.9
4.
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 }.
5.
Show that HAMPATH ≤P ANY-HAMPATH,
where
HAMPATH = { <D, s, t> : digraph D has a Hamiltonian directed path from s to t }
and
ANY-HAMPATH = { <D> : digraph D contains some Hamiltonian directed path }.