We present an algorithm that can efficiently compute a broad class of
inferences for discrete-time imprecise Markov chains, a generalised type of
Markov chains that allows one to take into account partially specified
probabilities and other types of model uncertainty. The class of inferences
that we consider contains, as special cases, tight lower and upper bounds on
expected hitting times, on hitting probabilities and on expectations of
functions that are a sum or product of simpler ones. Our algorithm exploits the
specific structure that is inherent in all these inferences: they admit a
general recursive decomposition. This allows us to achieve a computational
complexity that scales linearly in the number of time points on which the
inference depends, instead of the exponential scaling that is typical for a
naive approach