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{0 i1 j2 k | 0 <= i <= j <= k }

Is it possible to design a PDA for this language?

I think the answer is no, and it can only be defined using at least a context free grammar.

However, I don't know why. I need some discussion and explanation regarding this.

NBN
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  • See http://stackoverflow.com/questions/2597124/context-free-language-question-pumping-lemma – ComputerDruid Dec 02 '14 at 23:51
  • @ComputerDruid thanks for the note. I didn't know about the Ogden's lemma. However, I do want to know why there can't be a PDA for this language. I think it would be somehow possible to design a PDA, it would be hard I think but still possible. – NBN Dec 03 '14 at 00:00

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The answer is no. Actually there are neither a CFG nor an NPDA for this language. The proof can be established using a pumping lemma for context free languages.

Hassan Abbasi
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