Abstract: We define rationally additive semirings that are a generalization of ()complete and (-)continuous semirings. We prove that every rationally additive semiring is an iterat...
a more abstract characterisation in the setting of semirings. Formally, a domain semiring is a semiring S extended by a domain operation d : S → S which, for all x, y ∈ S, sati...
: We investigate weighted automata with discounting and their behaviours over semirings and finitely generated graded monoids. We characterize the discounted behaviours of weighted...
We introduce a weighted logic with discounting and we establish B¨uchi’s and Elgot’s theorem for weighted automata over finite words and arbitrary commutative semirings. The...
Simulations of weighted tree automata (wta) are considered. It is shown how such simulations can be decomposed into simpler functional and dual functional simulations also called f...