On the translation of languages from left to right
TLDR
LR(k) grammars are defined, which are perhaps the most general ones of this type, and they provide the basis for understanding all of the special tricks which have been used in the construction of parsing algorithms for languages with simple structure, e.g. algebraic languages.Abstract:
There has been much recent interest in languages whose grammar is sufficiently simple that an efficient left-to-right parsing algorithm can be mechanically produced from the grammar. In this paper, we define LR(k) grammars, which are perhaps the most general ones of this type, and they provide the basis for understanding all of the special tricks which have been used in the construction of parsing algorithms for languages with simple structure, e.g. algebraic languages. We give algorithms for deciding if a given grammar satisfies the LR(k) condition, for given k, and also give methods for generating recognizes for LR(k) grammars. It is shown that the problem of whether or not a grammar is LR(k) for some k is undecidable, and the paper concludes by establishing various connections between LR(k) grammars and deterministic languages. In particular, the LR(k) condition is a natural analogue, for grammars, of the deterministic condition, for languages.read more
Citations
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References
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Syntactic Analysis and Operator Precedence
TL;DR: Three increasingly restricted types of formal grammar are phrase structure Grammars, operator grammars and precedence grammar, which form models of mathematical and algorithmic languages which may be analyzed mechanically by a simple procedure based on a matrix representation of a relation between character pairs.
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Deterministic context free languages
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TL;DR: Bounded context grammars form models for most languages used in computer programming, and many methods of syntactic analysis, including analysis by operator precedence, are special cases of bounded context analysis.
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Universality of Tag Systems with P = 2
John Cocke,Marvin Minsky +1 more
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