Question

Given a language L, etc.

Show that the language L is a regular language.

To show that the language L is a regular language - find/design a
dfa that recognizes the language L.

Given a regular expression r, etc.

What is the language L, L = L(r)?

L(r) is the set of all strings etc.

Answer #1

Please increase your Brightness.....

L={ab (a+b)^n} where n>=0}

Every string in this language satrts with ab. So minimum number of states we required to construct a DFA are (2+2) 4.

Note : I have provided you needed information.If you have any doubt please comment. If you are satisfied with my answer please upvote. . .

Let Σ = {a}, and let L be the language
L={an :nisamultipleof3butnisNOTamultipleof5}.
Is L a regular language? HINT: Maybe instead of an explicit DFA
or regular expression, you can find another argument.

Prove by induction on n that if L is a language and R is a
regular expression such that L = L(R) then there exists a regular
expression Rn such that L(Rn) = L n. Be sure to use the fact that
if R1 and R2 are regular expressions then L(R1R2) = L(R1) ·
L(R2).

Show a regular expression representing the described set:
a). The set of strings of odd length over {s,t,r,i,n,g}
containing exactly 3 n's.

Let L ⊆ Σ* be a regular language. Suppose a ∈ Σ and
define L\a = {x : ax ∈ L }. Show that L\a is regular.

Find a regular expression to describe:
The set of all strings over the alphabet {a, b, c, d}
that contain exactly one a and exactly one b
So, for example, the following strings are in this
language:
ab, ba, cccbad, acbd, cabddddd, ddbdddacccc
and the following strings are NOT in this
language:
a, ccbc, acbcaaacba, acacac, bcbbbbbca, aca, c, d,
b

5 A Non-Regular language
Prove that the language}L={www∣w∈{0,1}∗} is not regular.

Design a DFA accepting the language of all strings over Σ = {0,
1} with the property that the number of 0s and the number of 1s in
a string are both odd.

For each of the following regular expressions, give 2 examples
of strings that are in the language described by the regular
expression, and 2 examples of strings that are not in that
language. In all cases the alphabet is {a,b}.
ab*ba*
(a ∪ ε)b*
(a ∪ b)ε*(aa ∪ bb)

For Automata class:
Let L be a regular language over the binary alphabet. Consider
the following language over the same alphabet: L' = {w | |w| = |u|
for some u ∈ L}. Prove that L' is regular.

Consider the language L = { w w : w ∈ { 0 , 1 } ∗ } is not
context-free. Note that this is the language of all strings that
consist of some combination of 0s and 1s, followed immediately by
that same combination of 0s and 1s. For example, 0101, 101101, and
110110 are all in the language because they consist of a string
followed by itself. Can you build a PDA to recognize this language?
(Hint: you...

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