Vitor Greati

A well-quasi-ordered (wqo) set generalizes the notion of well-foundedness and is a powerful tool for analyzing the complexity of computational problems through upper bounds on the length of controlled bad sequences, known as length theorems. The finitary multiset extension of a wqo-set induces an ordering on finite multisets over elements of that set, where one multiset precedes another if there exists an injective mapping between their elements that preserves the original ordering. In this work, we refine existing length theorems for the finitary multiset extension of Higman’s ordering over finite alphabets, and we establish a matching lower bound. As a corollary, we obtain tighter length bounds for the majoring extension of Higman’s ordering over finite alphabets. We demonstrate the application of our results in the complexity analysis of noncommutative hypersequent logics.