Balancing Straight-Line Programs for Strings and Trees

Abstract

The talk will explain a recent balancing result according to which a context-free grammar in Chomsky normal form of size m that produces a single string w of length n (such a grammar is also called a straight-line program) can be transformed in linear time into a context-free grammar in Chomsky normal form for w of size mathcal {O}(m), whose unique derivation tree has depth mathcal {O}(log n). This solves an open problem in the area of grammar-based compression, improves many results in this area and greatly simplifies many existing constructions. Similar balancing results can be formulated for various grammar-based tree compression formalism like top DAGs and forest straight-line programs. The talk is based on joint work with Moses Ganardi and Artur Jeż. An extended abstract appeared in [11]; a long version of the paper can be found in [12].