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Sep 12, 2017 at 20:55 comment added matheussilvapb My teacher always asks to make grammars without $\varepsilon$ productions, I think that's a good exercise.
Sep 12, 2017 at 20:35 comment added Yuval Filmus My grammar is context-free (some people disallow $\epsilon$ transitions so that a CFG would automatically be a CSG, but that's not the only choice possible). It is, however, extremely simple to get rid of the $\epsilon$ production. The resulting grammar is $S\to aSa|bSb|aTb|bTa|ab|ba$, $T\to aT|bT|a|b$.
Sep 12, 2017 at 19:49 comment added matheussilvapb Thanks, your grammar is way simpler than mine, but I think the idea is the same. Actually your grammar is a type-0 grammar due to that $\varepsilon$-transition, I wonder if you can make it without that.
Sep 12, 2017 at 19:43 history answered Yuval Filmus CC BY-SA 3.0