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The complexity of testing whether a finite-state (sequential or concurrent) probabilistic program satisfies its specification expressed in linear temporal logic. For sequential programs an exponential-time algorithm is given and it is shown that the problem is in PSPACE; this improves the previous upper bound by two exponentials and matches the known lower bound. For concurrent programs is is shown that the problem is complete in double exponential time, improving the previous upper and lower bounds by one exponential each. These questions are also addressed for specifications described by omega-automata or formulas in extended temporal logic.