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Knuth: LR grammars and left-to-right parser construction

Contribution grade

Deterministic parsing · Deterministic parsing

Reference score170,000Provisional editorial estimate of this exact contribution; its grade is assessed separately.

What changed

LR(k) formalizes unique prefix/lookahead-driven reductions and connects a fixed-k grammar test with finite state-set shift/reduce recognizer construction.

Scientific scope

LR(k) formalizes unique prefix/lookahead-driven reductions and connects a fixed-k grammar test with finite state-set shift/reduce recognizer construction. The LR(k) condition belongs to a grammar with specified lookahead k; two grammars for the same language may differ. Linear parsing claims concern input length for a fixed grammar/parser, and do not bound parser-construction cost or table size. Not all context-free grammars qualify. The whole deterministic-language and unspecified-lookahead undecidability proofs are outside this selected reading.

Evidence

Source-linked, scoped account of the original work. The published scope states the scientific assumptions and remaining verification limits. WRS has not independently certified the full proof, experimental result or system benchmark.

Contributors

Provisional WRS assessment, edition 2026-10-16.1. Independent expert calibration is pending. This grade does not certify correctness or assign ownership.

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