We show how prefix probabilities can be computed for stochastic linear indexed grammars (SLIGs). Our results apply as well to stochastic tree-adjoining grammars (STAGs), due to their equivalence to SLIGs. 1 Introduction The problem of computing prefix probabilities for stochastic context-free languages is defined as follows. Given a word sequence a 1 \Delta \Delta \Delta a n over some alphabet \Sigma, which we call the input prefix, we must compute quantity P w2\Sigma Pr(a 1 \Delta \Delta \Delta a n w). This problem has been discussed in [1, 4] with the main motivation of applications in speech recognition, where we are given some word sequence a 1 \Delta \Delta \Delta a n\Gamma1 , and must hypothesize the next word a n . The main idea leading to the solution of this problem is that all parts of context-free derivations that are potentially of unbounded size are captured into a set of equations that can be solved "off-line", i.e., before a specific prefix is considered. This is po..