Let L be a language over an input and if TM 'T' (Turing machine T) excepts every woed in L and rejects every word of L' it is called as recursive language.

Example :

1. String ends with '101'

2. Number of 'a'= number of 'b'

   Accept(T) = L
   
   Reject(T) = L'
   
   Loop(T) = ϕϕ
   
   ϕ = nullϕ = null
   

Recursive enumeration language : Let L be a langauage over an input, and if TM 'T' excepts every word of L and rejects or loops every word in L' then it is called recursive enumeration language.

Example :

anbnanbn

Accept(T) = L

Reject(T) + Loop(T) = L'