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Hierarchy of LL(k) language examples

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In order to illustrate the hierarchy of LL(k) languages, could someone give a family of example languages (Lk)k∈ℕ such that Lk is LL(k+1), but not LL(k)? Rosenkrantz and Stearns prove (on p.247) that { an (bkd + b + cc)n | n≥1 } is not LL(k); however, it is not clear whether it is LL(k+1). Moreover, there may be easier language examples? - Jochen Burghardt (talk) 11:49, 25 February 2015 (UTC)[reply]