Question

****** Theory of Computing *********

1. Provide a regular expression for “all even length strings of b’s”.

2. List all words of length 4 in Language((a+b)* a). Also, provide an English description of this language.

Answer 1

1.

If the alphabet Σ = (b) then,

the regular expression for all the even length strings of b is

R = (bb)*.

Here, ε is considered to be of even length.

2.

The regular expression for the language given is (a+b)*a.

To get the list of words of length 4 from the language, the following steps are taken :

List out all the strings of length 4 possible from the alphabet of Σ (a,b). This can be done by treating 0 in a truth table as symbol a and 1 in the truth table as symbol b. So, for strings of length, a combination of 2⁴ = 16 are made as in a truth table.

aaaa

aaab

aaba

aabb

abaa

abab

abba

abbb

baaa

baab

baba

babb

bbaa

bbab

bbba

bbbb

Step 2 :

Extract only those strings that end with symbol a.

So, the strings of length 4 are :

aaaa

aaba

abaa

abba

baaa

baba

bbaa

bbba

The language described by the given regular expression is used to denote the set of all strings that end with symbol a.