Comparison  Recursive Language  Recursively enumerable language 
Also Known as  Turing decidable languages  Turing recognizable languages 
Definition  In Recursive Languages, the Turing machine accepts all valid strings that are part of the language and rejects all the strings that are not part of a given language and halt.  In Recursively enumerable languages, the Turing machine accepts all valid strings that are part of the language and rejects all the strings that are not part of the given language but do not halt and starts an infinite loop. 
States  (1) Halt and accept
(2) Halt and Reject

(3) Halt and accept
(4) Halt and Reject (5) Never Halt (Infinite loop) 
Loop  Finite Loop  Infinite loops of machine are possible 
Halting  Halting Turing Machine  Non Halting Turing Machine 
Accept/ Reject  Accept (Turing machine) = L Reject (Turing machine) = L^{‘} Loop (Turing machine) = φφ φ = null φ = null 
Accept (Turing machine) = LReject (Turing machine) + Loop (Turing machine) = L’ 
Closed under  Closed under all except homomorphism, substitution, GSM mapping, and rational transduction  Closed under all except set difference, and complementation. 
contextsensitive language  RE languages or type0 language 
FAQ about Recursive languages closure properties
Properties of Recursively enumerable languages
 Recursive Languages Closed Under union.
 Recursive Languages Closed Under intersection.
 Recursive Languages Closed Under set difference.
 Recursive Languages Closed Undercomplementation.
 Recursive Languages Closed Under intersection with a regular language.
 Recursive Languages Closed Under concatenation.
 Recursive Languages Closed Under Kleene star.
 Recursive Languages Closed Under Kleene plus.
 Recursive Languages Closed Under reversal.
 Recursive Languages Closed Under λλfree homomorphism.
 Recursive Languages Recursive Languages Not Closed Under homomorphism.
 Recursive Languages Closed Under inverse homomorphism.
 λλfree substitution Recursive Languages Closed Under λλfree substitution.
 Recursive Languages Not Closed Under substitution.
 Recursive Languages Closed Under λλfree GSM mapping.
 Recursive Languages Not Closed Under GSM mapping.
 Recursive Languages Closed Under inverse GSM mapping.
 Recursive Languages Not Closed Under rational transduction.
FAQ about Recursively Enumerable languages closure properties?
 Recursively enumerable languages Closed under union.
 Recursively enumerable languages Closed under intersection.
 Recursively enumerable languages Not Closed under set difference.
 Recursively enumerable languages Not Closed under complementation.
 Recursively enumerable languages Closed under intersection with a regular language.
 Recursively enumerable languages Closed under concatenation.
 Recursively enumerable languages Closed under Kleene star.
 Recursively enumerable languages Closed under Kleene plus.
 Recursively enumerable languages Closed under reversal.
 Recursively enumerable languages Closed under λλfree homomorphism.
 Recursively enumerable languages Closed under homomorphism.
 Recursively enumerable languages Closed under inverse homomorphism.
 Recursively enumerable languages Closed under λλfree substitution.
 Recursively enumerable languages Closed under substitution.
 Recursively enumerable languages Closed under λλfree GSM mapping.
 Recursively enumerable languages Closed under GSM mapping.
 Recursively enumerable languages Closed under inverse GSM mapping.
 Recursively enumerable languages Closed under rational transduction.