Let L = L1 ∩ L2 where L1 and L2 are language defined below :

L1 = {ambmc an bn m, n ≥ 0}

L2 = {aibj ck | i, j, k ≥ 0}

Then L is : 

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  1. Not Recursive
  2. Regular 
  3. Context Free but not regular 
  4. Recursively enumerable but not context free

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Option 1 : Not Recursive
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The correct answer is Not Recursive.

key-point-imageKey Points

  • Let L = L1 ∩ L2 where L1 and L2 are languages defined below :
    • L1 = {ambmcanbn | m, n ≥ 0}
    • L2 = {aibjck | i, j, k ≥ 0}
  • The intersection of these two languages is a language L where the number of a's is equal to the number of b's and the number of c's is equal to the number of b's.
  • This language is not recursive because it cannot be decided by a Turing machine in a finite amount of time.

additional-information-imageAdditional Information

  • A recursive language is a type of formal language that can be decided by a Turing machine that always halts.
  • A language is considered recursively enumerable if there is a Turing machine that will halt and accept the strings in the language but may run forever for strings not in the language.
  • Regular languages can be recognized by finite automata and are a subset of context-free languages.
  • Context-free languages can be recognized by pushdown automata and include most programming languages.
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