Balancing Straight-line Programs

We show that a context-free grammar of size produces single string $w$?> length $n$?> (such is also called straight-line program) can be transformed in linear time into for $\mathcal {O}(m)$?> , whose unique derivation tree has depth {O}(\log n)$?> . This solves an open problem the area grammar-based compression, improves many results this area, and greatly simplifies existing constructions. Similar are shown two formalisms compression: top dags forest programs. These balancing all deduced from meta-theorem stating algebraic circuit over algebra with certain finite base property reduced to cost constant multiplicative increase. Here, refers unfolding (or unravelling) circuit. In particular, applies standard arithmetic circuits (noncommutative) semirings.