Parameter reduction and automata evaluation for grammar-compressed trees

  • Authors:

  • Markus Lohrey;Sebastian Maneth;Manfred Schmidt-Schauí

  • Affiliations:

  • Universität Leipzig, Institut für Informatik, Germany;NICTA and University of New South Wales, Australia;Goethe-Universität Frankfurt, Institut für Informatik, Germany

  • Venue:
  • Journal of Computer and System Sciences
  • Year:
  • 2012

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Abstract

Trees can be conveniently compressed with linear straight-line context-free tree grammars. Such grammars generalize straight-line context-free string grammars which are widely used in the development of algorithms that execute directly on compressed structures (without prior decompression). It is shown that every linear straight-line context-free tree grammar can be transformed in polynomial time into a monadic (and linear) one. A tree grammar is monadic if each nonterminal uses at most one context parameter. Based on this result, polynomial time algorithms are presented for testing whether a given (i) nondeterministic tree automaton or (ii) nondeterministic tree automaton with sibling-constraints or (iii) nondeterministic tree walking automaton, accepts a tree represented by a linear straight-line context-free tree grammar. It is also shown that if tree grammars are nondeterministic or non-linear, then reducing their numbers of parameters cannot be done without an exponential blow-up in grammar size.