Cross-moments computation for stochastic context-free grammars

In this paperwe consider the problemof efficient computation of cross-moments of a vector randomvariable represented by a stochastic context-free grammar. Two types of cross-moments are discussed. The sample space of the first one is the set of all derivations of the context-free grammar, and the sample space of the second one is the set of all derivations which generate a string belonging to the language of the grammar. In the past, this problem has beenwidely studied, but mainly for the cross-moments of scalar variables and up to the second order. This paper presents new algorithms for computing the cross-moments of an arbitrary order, and the previously developed ones are derived as special cases.