  Under some mild Markov assumptions it is shown that the problem of designing
optimal sequential tests for two simple hypotheses can be formulated as a
linear program. The result is derived by investigating the Lagrangian dual of
the sequential testing problem, which is an unconstrained optimal stopping
problem, depending on two unknown Lagrangian multipliers. It is shown that the
derivative of the optimal cost function with respect to these multipliers
coincides with the error probabilities of the corresponding sequential test.
This property is used to formulate an optimization problem that is jointly
linear in the cost function and the Lagrangian multipliers and an be solved for
both with off-the-shelf algorithms. To illustrate the procedure, optimal
sequential tests for Gaussian random sequences with different dependency
structures are derived, including the Gaussian AR(1) process.
