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I’m not an expert on this topic, but I found these course notes (including some bibliographical references) which state that the language L = {xn : n ∈ ℕ} ∪ {xnyn : n ∈ ℕ} has no LL(k) parser, while being deterministic context-free (see pp. 24 and 27).

Edit: I found a better reference. The paper Two iteration theorems for the LL(k) languages by J.C. Beatty contains a proof that the LR language L = {anbn, ancn : n ≥ 1} is not LL (see Theorem 5.2).

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I’m not an expert on this topic, but I found these course notes (including some bibliographical references) which state that the language L = {xn : n ∈ ℕ} ∪ {xnyn : n ∈ ℕ} has no LL(k) parser, while being deterministic context-free (see pp. 24 and 27).

Edit: Maybe I found a better reference. The paper Two iteration theorems for the LL(k) languages by J.C. Beatty seems to contain contains a proof that some language L = {anbn, ancn : n 1} is LR but not LL (I say seems to contain because I can’t access that paper, but I found it via a search on Google)see Theorem 5.2).

2 added 406 characters in body

I’m not an expert on this topic, but I found these course notes (including some bibliographical references) which state that the language L = {xn : n ∈ ℕ} ∪ {xnyn : n ∈ ℕ} has no LL(k) parser, while being deterministic context-free (see pp. 24 and 27).

Edit: Maybe I found a better reference. The paper Two iteration theorems for the LL(k) languages by J.C. Beatty seems to contain a proof that some language is LR but not LL (I say seems to contain because I can’t access that paper, but I found it via a search on Google).

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