Abstract. This paper considers the verification of continuous-time Markov decision process (CTMDPs) against single-clock deterministic timed automata (DTA) specifications. The central issue is to compute the maximum probability of the set of timed paths of a CTMDP C that are accepted by a DTA A. We show that this problem can be reduced to a linear programming problem whose coefficients are maximum timed reachability probabilities in a set of CTMDPs, which are obtained via a graph decomposition of the product of the CTMDP C and the region graph of the DTA A.