Question
Download Solution PDFLet 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 :
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFThe correct answer is Not Recursive.
Key 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
- 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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