CS 381 Homework 5 Solutions
Fall 2006
September 29, 2006
1:
The set consists of strings of blocks of 0’s and 1’s where each block is separated
by a 2; each block can have any combination of 0’s and 1’s; the length of each
successive block is one greater than the previous block; the first block is of
length 1; the strings end in a 2; there are an even number of blocks; there are a
minimum of 2 blocks.
2:
We assume that the alphabet of L and M are disjoint. If they are not disjoint, we
can simply do a homomorphism to the alphabet of one of the languages and add
hats for example. Then we just do the corresponding inverse homomorphism at
the end to remove these hats.
We define the homomorphism h
1
as follows:
L
a
a
a
h
Σ
∈
∀
=
)
(
1
M
b
b
h
Σ
∈
∀
=∈
)
(
1
Then
)
(
1
1
L
h
−
is the language containing strings in L with symbols from the
alphabet of M arbitrarily inserted. Similarly define the homomorphism h2 as:
M
b
b
b
h
Σ
∈
∀
=
)
(
2
L
a
a
h
Σ
∈
∀
=∈
)
(
2
Therefore the desired language alt(L,M) is obtained as:
*
)
(
)
(
)
(
)
,
(
1
2
1
1
M
L
M
h
L
h
M
L
alt
Σ
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Fall '06
 HOPCROFT
 Formal language, Regular expression, Regular language, Nondeterministic finite state machine, Pumping lemma for regular languages

Click to edit the document details