Mathematical systems theory

, Volume 11, Issue 1, pp 317–325 | Cite as

A generalization of leftmost derivations

  • Mark Luker


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.


Computational Mathematic Analogous Result Single Production Leftmost Derivation 
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  1. 1.
    B. Baker, Non-context-free grammars generating context-free languages,Information and Control 24 (1974), 231–246.Google Scholar
  2. 2.
    R. J. Evey, The theory and application of pushdown store machines,Harvard Univ. Comp. Lab. Report NSF-10, May 1963.Google Scholar
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    S. Ginsburg,The Mathematical Theory of Context-Free Languages, McGraw Hill, New York, 1966.Google Scholar
  4. 4.
    S. Ginsburg andE. H. Spanier, Control sets on grammars,Mathematical Systems Theory 2 (1968), 159–177.Google Scholar
  5. 5.
    M. Luker, A characterization of the derivation-bounded languages (to be submitted for publication).Google Scholar

Copyright information

© Springer-Verlag New York Inc 1978

Authors and Affiliations

  • Mark Luker
    • 1
  1. 1.University of MinnesotaDuluthUSA

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