Homework 5 Solutions
1) 4-leaf spanning tree (4L-ST) is in NP:
Given an undirected graph G = (V, E ), we can determine whether a subgraph H = (V, F ) of G is connected
by simple DFS or BFS which are O(|V | + |F |) so this part is polynomial. We ca
CSE 555 MIDTERM EXAMINATION SOLUTIONS
TAKE-HOME: OUT 02/21 NOON, DUE 02/25 NOON
The completed test is to be submitted electronically to firstname.lastname@example.org before
the deadline, or time-stamped by the main oce in CIDSE and placed in Prof.
Colbourns physical m
Homework 4 Solutions
1) If there are any tiles with the same number of symbols on top and bottom (so that the top is exactly the
bottom), clearly there is a match.
Otherwise, if we have only tiles with more symbols on top than bottom, or only tile
Homework 3 Solutions
1) First, here are some expressions that will be used in the problems.
P LU S (a, a, a) is synonymous with a = 0 and so P LU S (a, a, a) is synonymous with a = 0.
x(P LU S (a, x, b) is synonymous with a b and x(P LU S (a, x, b
Homework 2 Solutions
1a) The following TM R is a recognizer for DOU BCF G :
R = On input G where G is a CFG
Let E be an enumerator for the regular (and thus recognizable) language that prints each w
in lexicographic order (length non-decreasing,
Homework 1 Solutions
1) ALLON EDF A is decidable. Idea: If 1 L(M ), then there is no string from 1 in L(M ) so we can
equivalently check the emptiness of the language 1 L(M ).
Proof: The following TM T decides ALLON EDF A .
T = On input M where M