Parameter Reduction in Grammar-Compressed Trees

Abstract. Trees can be conveniently compressed with linear straight-line contextfree 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, a polynomial time algorithm is presented for testing whether a given nondeterministic tree automaton with sibling constraints accepts a tree given by a linear straight-line context-free tree grammar. It is 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.

• Type: Conference
• Year: 2009
• Where: FOSSACS
• Authors: Markus Lohrey, Sebastian Maneth, Manfred Schmidt-Schauß
• Keywords: Applied Computing, Context-free Tree Grammar, FOSSACS 2009, Straight-line Context-free Tree, Tree Grammars