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I have to decide for several languages whether they are regular, context-free, det. context-free or type-0. I understand how to show a language not to be regular (using the pumping lemma), but how to decide it for the other language types very fast? The first language is

{a,b,c}* \ {a^n b^n c^n | n is element of natural numbers}

jannnik
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  • "I understand how to show a language to be regular (using the pumping lemma)" -- **NO** Pumping lemma **doesn't** shows that a language **is** a regular language. Pumping lemma shows that a language is **not** a regular language. **Pumping lemma is necessary but not a sufficient property for regular language**. – Grijesh Chauhan Mar 04 '15 at 06:54
  • Thanks for your comment. It was a wording mistake, of course the pumping lemma shows that a language is not regular. Do you have a solution for my whole problem? – jannnik Mar 05 '15 at 11:29
  • I think you need something like `language -- [ tool ] --> 'type of language'` ?? – Grijesh Chauhan Mar 05 '15 at 11:43
  • Yes, but I have to find out the language type by hand in an exam. The questions are possibly multiple choice. – jannnik Mar 05 '15 at 12:09
  • yes, that is what for this whole subject is - classification of formal languages - theory of formal language. check [this](http://stackoverflow.com/a/13648491/1673391). – Grijesh Chauhan Mar 05 '15 at 12:21

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