cs 402 lecture 3

Regular Expression (RE)
a* and a+ are the regular expressions of the Language L1 and L2
Recursive Regular Expressions :

Step 1 : Every letter of sigma E including null string is a regular expression.
Step 2 : If r1 and r2 are regular expressions then
i (r1)
ii r1 r2
iii r1+r2
iv r1* 
are also regular expressions.
Step 3: Nothing else is a regular expression.

Express any language in short way  as regular expressions.

One language has more than one regular expressions but one regular expression can make only one language.

CS402 Lecture 2

Automaton :
The procedure to achieve the specific goal or task, according to our requirements.
1. Finite Automaton :
Possibilities are limited and created by us. Just like green light for go in the signal and red to stop in controlling traffic. And the given specific time to stop and start of each traffic.
Palindrome Language: 
The feature of this language is that it can be define with or without null string (Lamda)
String cannot be change if it is written in reverse order. And the line draws and shows the symmetry if read from both directions i.e aba
Even Length  String (middle line symmetric)
Odd Length  String (middle letter symmetric with same length)
If we combine two palindrome strings it create another palindrome.

Even Even Language:

Kleene Star closure
denoted by E* (Sigma star)
All concatenation of letters  and null string
Result will be in the strings two or more strings concatenate  result will be in between the string.

Plus operator :

It is just like kleene star but we cannot add null string by self in the plus operator

Recursive definition of languages :

The following steps are used to describe recursive languages.
1.some basic words are specified in the language
2. rules for constructing more words are defined in the language
3. no strings except those constructed above are allowed in the language