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Knuth defined LR(k) grammars through uniquely determined reductions with fixed lookahead. He connected that condition with finite methods for testing a specified grammar and generating stack-based shift/reduce recognizers. A parser reads the input while deciding when a recognized part should be reduced by a grammar production. LR(k) makes that decision depend on the parsed prefix and a fixed number of upcoming terminal symbols. Knuth organizes the relevant configurations into finite state sets and a stack recognizer, while explicitly noting potentially large state collections. Prior precedence/bounded-context work and later compact parser generators remain separately attributed.
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Scientific scope
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.
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People and systems
Donald E. Knuth
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English catalogue narrative
Knuth: LR grammars and left-to-right parser construction
Knuth defined LR(k) grammars through uniquely determined reductions with fixed lookahead. He connected that condition with finite methods for testing a specified grammar and generating stack-based shift/reduce recognizers.
A parser reads the input while deciding when a recognized part should be reduced by a grammar production. LR(k) makes that decision depend on the parsed prefix and a fixed number of upcoming terminal symbols. Knuth organizes the relevant configurations into finite state sets and a stack recognizer, while explicitly noting potentially large state collections. Prior precedence/bounded-context work and later compact parser generators remain separately attributed.
Scientific scope
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.
People and systems
Donald E. Knuth