On noiseless diagnosis

Let F be the fault of a system which takes value in Ω={f_i}, and p_i be the known probability of occurrence of f_i. Let T={t_j} be a sufficient set of tests available for diagnosing the system, and c_j be the cost of t_j. The number of possible responses for each test in T may be different. The author introduces the cost-entropy function as an information-theoretic lower bound on C_min the expected cost of an optimal testing tree. The author also obtains a universal upper bound of C_min when {p_i} is unknown, and a refined upper bound on C_min when {p_i} is known. The author´s results are essential for developing heuristic strategies to search for optimal and suboptimal testing trees