CS 341 Automata Theory
Elaine Rich
Homework 3
Due Thursday, September 21 at 11:00
1)
Give a clear English description of the language accepted by the following FSM:
b
1
b
2
a
3
a
a
b
a
a
4
b
5
6
a
,
b
2)
Construct a deterministic finite state machine to accept each of the following languages:
a)
The set of binary representations, without leading 0’s, of integers that are divisible by 4.
b)
The set of binary representations, without leading 0’s, of integers that are powers of 4.
c)
The set of binary strings that have at least one occurrence of the substring 001.
d)
The set of binary strings that have no substring 001.
e)
The set of binary strings with at most one pair of consecutive 0’s and at most one pair of
consecutive 1’s.
f)
The set of all binary strings with the property that none of its prefixes ends in 0.
g)
{
w
is an element of {
a
,
b
}*: #
a
(
w
) + 2#
b
(
w
) is divisible by 5}. (#
a
w
is the number of
a
’s in
w
).
3)
Construct a nondeterministic finite state machine to accept each of the following languages:
a)
{
w
∈
{
a
,
b
}* :
w
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 Fall '08
 Rich

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