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# Characterizing Non-Regularity

This paper considers a characterization of the context-free non-regular languages, conjecturing that there for all such languages exists a fixed string that can be pumped to exhibit infinitely many equivalence classes. A proof is given only for a special case, but the general statement is conjectured to hold. The conjecture is then employed to demonstrate the non-context-free nature of the shuffle of two context-free languages.

### Keywords

context-free, formal languages, pumping, pumping lemma, regular, shuffle

### Authors

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Entry responsible: Martin Berglund

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Page Responsible: Frank Drewes
2022-12-08