Weighted finite automata (WFA) are used with FPGA accelerating hardware to scan large genomic banks. Hardwiring such automata raises surface area and clock frequency constraints, requiring efficient ∊-transitions-removal techniques. In this paper, we present bounds on the number of new transitions for the development of acyclic WFA, which is a special case of the ∊-transitions-removal problem. We introduce a new problem, a partial removal of ∊-transitions while accepting short chains of ∊-transitions.