how this language is not recursive?

Question

This question was asked at Gate 2009. I don't understand how it's not recursive?

L = {A^m B^m C Aⁿ Bⁿ | m, n ≥ 0}
L' = {Aⁱ B^j C^k | i, j, k ≥ 0}

Why is language {L intersection L'} not recursive?

What grammar is this? PEG? BNF? What is "Gate 2009" and how does it pertain to this question? Simply tagging this with "automata" does not seem to be sufficient background for someone to understand the context in which you are asking this question. — Phrogz, Aug 25 '13 at 05:13
This looks recursive to me. We must be missing something vital. — user2357112, Aug 25 '13 at 05:14
@AnshikaAgrawal The downvotes indicate that others do not share your belief that it is a complete question. I advise you to edit and expand upon it, providing background on the question, and perhaps adding what you have thought about it so far. — Phrogz, Aug 25 '13 at 05:23
Try asking this at [computer science](http://cs.stackexchange.com/). — Kevin Panko, Aug 27 '13 at 18:22

score 1 · Answer 1 · answered Aug 25 '13 at 05:39

Since "recursive" is a general category of language that includes all simpler classes of language, the question is probably meant to be understood as why the given language is something simpler than a recursive language—say, that it is a type 1, 2, or 3. Otherwise the question makes no sense (since it's clearly recursive.)

The answer can be found by looking at the intersection:

L ∩ L' = {A^m B^m C | m ≥ 0}

This is just the language of all balanced parentheses followed by C, which can be recognized by a deterministic push-down automaton and hence is a context-free language.

how this language is not recursive?

1 Answers1