TA ASSIGNMENT 1 PART 3

Theory of Automata

Assignment #1

Part #3

Recursive Definition #11:

Language of Expressions having at least one operator defined on Σ={+,-,*,/,a,b} 

Step 1#- a+b ,a*b,a/b and a-b are in L

Step 2#- If x is in L then x+x,x-x,x*x,x/x is also in L

Step 3#- No words except generated above can be considered as member of Language.

Recursive Definition #12:

Language of string starting and ending on different alphabet defined on Σ={a,b}

Step 1#- ab and ba are in L

Step 2#- If x is in L then axb,and bxa are also in Σ*. 

Step 3#- No words except generated above can be considered as member of Language.

Recursive Definition #13:

Language of even numbers

Step 1#- 0 and 2 are in L

Step 2#- If x is in L then x+2 and x-2 is also in L. 

Step 3#- No words except generated above can be considered as member of Language.

Recursive Definition #14:

Language of negative integers defined on Σ={-1,-2,-3,-4,-5,-6,-7,-8,-9}

Step 1#- -1 and -2 are in L

Step 2#- If x is in L then x-1 is also in L. 

Step 3#- No words except generated above can be considered as member of Language.

Recursive Definition #15:

Language of Palindrome Σ={a,b}

Step 1#- A and B are Palindrome

Step 2#- If x is in Σ* then xRev(x) ,xarev(x) and xbRev(X) are also Palindrome.

Step 3#- No words except generated above can be considered as member of Language.