Variable-length block-coding schemes are investigated for discrete memoryless channels with ideal feedback under cost constraints. Upper and lower bounds are found for the minimum achievable probability of decoding error P_e, as a function of constraints R, , and τ̅ on the transmission rate, average cost, and average block length respectively. For given R and , the lower and upper bounds to the exponent -( P_e,)/τ̅ are asymptotically equal as τ̅→∞. The resulting reliability function, _τ̅→∞ (-

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... e,)/τ̅, as a function of R and , is concave in the pair (R, ) and generalizes the linear reliability function of Burnashev to include cost constraints. The results are generalized to a class of discrete-time memoryless channels with arbitrary alphabets, including additive Gaussian noise channels with amplitude and power constraints.