  This paper presents novel Weighted Finite-State Transducer (WFST) topologies
to implement Connectionist Temporal Classification (CTC)-like algorithms for
automatic speech recognition. Three new CTC variants are proposed: (1) the
"compact-CTC", in which direct transitions between units are replaced with
<epsilon> back-off transitions; (2) the "minimal-CTC", that only adds <blank>
self-loops when used in WFST-composition; and (3) the "selfless-CTC" variants,
which disallows self-loop for non-blank units. Compact-CTC allows for 1.5 times
smaller WFST decoding graphs and reduces memory consumption by two times when
training CTC models with the LF-MMI objective without hurting the recognition
accuracy. Minimal-CTC reduces graph size and memory consumption by two and four
times for the cost of a small accuracy drop. Using selfless-CTC can improve the
accuracy for wide context window models.
