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The concept of LL( k ) context-free grammars is extended to cooperating distributed (CD) grammar systems working in the = m -mode of derivation in a consistent way. Namely, every LL( k ) context-free language can be generated by an LL( k ) CD grammar system. Further fundamental properties of languages generated by LL( k ) CD grammar systems are proved, for instance their unambiguity and the capability of LL( k ) CD grammar systems to describe typical non-context-free languages, including even a non-semilinear language. Most importantly, a parsing algorithm with strictly sub-quadratic time complexity is presented for LL( k ) CD grammar systems.
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Bordihn et al. (2026) studied this question.
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