Design of context-free grammars for lossless data compression

Any context-free grammar G generates a language L(G). We are interested in context-free grammars G in which L(G) consists of exactly one string. Given a data string a: over a finite alphabet and a context-free grammar G such that L(G) = {x}, one call reduce G to a simpler grammar G' for which L(G') = {x} and for which certain constraints are satisfied. One then losslessly compresses x by losslessly compressing the grammar G'. The redundancy performance of this compression algorithm based upon reduced grammars is discussed.