Abstract
Quotient operators have been rarely studied in the context of weighted rational expressions and automaton generation—in spite of the key role played by the quotient of words in formal language theory. To handle both left- and right-quotients we generalize an expansion-based construction of the derived-term (or Antimirov, or equation) automaton and rely on support for a transposition (or reversal) operator. The resulting automata may have spontaneous transitions, which requires different techniques from the usual derived-term constructions.