A generalization of leftmost derivations

Luker, Mark

doi:10.1007/bf01768484

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“…In a previous paper [14], the concept of leftmost derivation was extended to depth-first derivation, and a result of Evey [4], that the leftmost derivations of an arbitrary phrase-structure grammar generate a context-free language, was generalized to depth-first derivations. In this paper, we investigate the interaction of depth-first derivations with control sets on grammars, which have been studied by numerous investigators [1-3, 5-8, 10, 12, 13, 15-19] using leftmost or arbitrary derivations.…”

Section: Introductionmentioning

confidence: 99%

Control sets on grammars using depth-first derivations

Luker

1979

Math. Systems Theory

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Abstract. Control sets on grammars are extended to depth-first derivations. It is proved that a context-free language is generated by the depth-first derivations of an arbitrary context-free grammar controlled by an arbitrary regular set. This result is sharpened to obtain a new characterization of the family of derivation-bounded languages: a language L is derivation bounded if and only if it is generated by the depth-first derivations of a context-free grammar G controlled by a regular subset R of the Szilard language of G. The left-derivation-bounded languages are characterized analogously using leftmost derivations. It is proved that a grammar G is nonterminal bounded if and only if the Szilard language defined using only the depth-first derivations of G is regular. Finally, it is proved that if a family of languages C is a trio, a semi-AFL, an AFL, or an AFL closed under k-free substitution, then the family of languages generated using arbitrary context-free grammars controlled by members of C is full, is closed under reversal, and has the closure properties assumed of C.

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Section: Introductionmentioning

confidence: 99%