A mathematical approach to multi-pass parsing

  • Berthold Hoffmann
  • Ilse -R. Schmiedecke
Part of the Lecture Notes in Computer Science book series (LNCS, volume 88)


Derivations from Two-Level Grammars have been defined only in terms of the infinite context-free grammars that can be generated from them. This fact has proven a severe theoretical obstacle to solving the parsing problem for two-level grammars. So far, partial solutions exist for Van Wijngaarden Grammars, Extended Affix Grammars, and Affix Grammars which allow parsing in a single pass from left to right, because these special cases could be handled without developing a full theory of parsing for two-level grammars.

In this paper, we propose a new theory of Extended Affix Grammar derivations. The key idea is to use a graph grammar for modelling the two-level derivation process. This allows us to give a precise definition of a parse, which applies correctly to any well-formed Extended Affix Grammar. The concept of multi-pass parsing originates from practical compiler design, where parses are organized as a sequence of passes in order to avoid random access to the full parse tree. We demonstrate how this concept can be incorporated into our theoretical framework by means of canonical graph derivations. This allows us not only to establish the adequacy of the multi-pass approach, but can also be used as a complexity measure for Extended Affix Grammars.


Extended Affix Grammars Graph Grammars Two-Level Derivations Parsing Passes Pass-Complexity 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1980

Authors and Affiliations

  • Berthold Hoffmann
    • 1
  • Ilse -R. Schmiedecke
    • 1
  1. 1.TU Berlin, DFG-Projekt EAGLEBerlin 10

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