Hypothesis testing with the general source

The asymptotically optimal hypothesis testing problem, with general sources as the null and alternative hypotheses, is studied under exponential-type error constraints on the first kind of error probability. Our fundamental philosophy is to convert all of the hypothesis testing problems to the pertinent computation problems in the large deviation-probability theory. This methodologically new approach enables us to establish compact general formulas of the optimal exponents of the second kind of error and correct testing probabilities for the general sources including all nonstationary and/or nonergodic sources with arbitrary abstract alphabet (countable or uncountable). These general formulas are presented from the information-spectrum point of view.