A drawback of the simple greedy inference algorithm in Connectionist Temporal Classification (CTC) is that it maximizes the probability of a single alignment rather than the final output sequence. To find the optimal output sequence, the inference algorithm should choose the output $Y$ that has the maximum conditional probability by marginalizing over all alignments $A$ that produce $Y$. Mathematically, the probability of an output sequence is $P_{CTC}(Y|X)=\sum_{\text{all A that produce Y}}p(A|X)$, and the optimal sequence is $\hat{Y}=\text{argmax}_{\text{all possible Y}} P_{CTC}(Y|X)$.