Rigorous approximated determinization of weighted automata

In this paper we study approximated determinization of WFAs. We describe an algorithm that, given a WFA A and an approximation factor t≥1, constructs a DWFA A′ that t-determinizesA. Formally, for all words w∈Σ∗, the value of w in A′ is at least its value in A and at most t times its value in A. Our construction involves two new ideas: attributing states in the subset construction by both upper and lower residues, and collapsing attributed subsets whose residues can be tightened. The larger the approximation factor is, the more attributed subsets we can collapse. Thus, t-determinization is helpful not only for WFAs that cannot be determinized, but also in cases determinization is possible but results in automata that are too big to handle. We also describe a property (the t-twins property) and use it in order to characterize t-determinizable WFAs. Finally, we describe a polynomial algorithm for deciding whether a given WFA has the t-twins property.