Abstract
A generalization of leftmost derivation called depth-first derivation is defined. The main result, that the depth-first derivations of an arbitrary phrase-structure grammar generate a context-free language, is proved using a new technique in which families of equivalent depth-first derivations of one grammar are represented by single productions in a new grammar. This result is related to several others, including an analogous result for leftmost derivations, through the theorem of B. Baker [1] that every terminal-bounded grammar generates a context-free language.
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References
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M. Luker, A characterization of the derivation-bounded languages (to be submitted for publication).
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Luker, M. A generalization of leftmost derivations. Math. Systems Theory 11, 317–325 (1977). https://doi.org/10.1007/BF01768484
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DOI: https://doi.org/10.1007/BF01768484