CMPS 260 Spring 2024
HW #1: Designing DFA's
Due: 2pm, Wednesday, Jan. 31
For each problem, you are to present a DFA
(in the form of a transition diagram) that accepts the
described language. If the alphabet is not explicitly indicated,
assume that it is {a,b}.
1.
The language
containing precisely those strings
whose first and last symbols are different
(i.e., one of them is a and the other is b).
2.
The language
containing precisely those strings having
an even number of occurrences of a and
at least three occurrences of b.
Expressed using a set former:
{ x ∈ {a,b}* | #a(x) is even
∧ #b(x) is at least three }
3.
The language
containing precisely those strings
having aab as a substring.
Expressed using a set former:
{ xaaby | x,y ∈ {a,b}* }
4.
The language
containing precisely those strings
not having aba as a substring.
5.
The intersection of the languages in Problems 3 and 4.
That is, the set of strings
having aab as a substring but
not having aba as a substring.