Dealing with Hardware Space Limits when Removing " - Transitions in a WFA

Weighted Finite Automata (WFA) over (max; +)-semirings are used for pattern matching in genomic databanks with substitution costs. They can be eeciently parsed using reconngurable hardware like FPGAs (Field Programmable Gate Arrays) implementing the linear encoding scheme. In biological applications, one wants to double every regular transition with an "-transition to modelize deletions. Critical paths in the F-PGA prevent chains of "-transitions from being arbitrarily large, so the "-transitions must be removed. Generic "-transitions-removal algorithms produce too many new transitions. We propose an analysis of the "-transitions-removal under a condition of path-equivalence. In particular, we give a constructive way to remove the "-transitions on the linear-shaped parts of a WFA and an optimal bound of the number of new transitions produced.