The bottleneck in the quantitative analysis of Markov chains and Markov
decision processes against specifications given in LTL or as some form of
nondeterministic B\"uchi automata is the inclusion of a determinisation step of
the automaton under consideration. In this paper, we show that full
determinisation can be avoided: subset and breakpoint constructions suffice. We
have implemented our approach---both explicit and symbolic versions---in a
prototype tool. Our experiments show that our prototype can compete with mature
tools like PRISM.Comment: 38 pages. Updated version for introducing the following changes: -
general improvement on paper presentation; - extension of the approach to
avoid full determinisation; - added proofs for such an extension; - added
case studies; - updated old case studies to reflect the added extensio
