Two-way cost automata and cost logics over infinite trees
Achim Blumensath, Thomas Colcombet, Denis Kuperberg, Paweł Parys, Michael Vanden Boom · 2014
Regular cost functions provide a quantitative extension of regular languages that retains most of their important properties, such as expressive power and decidability, at least over finite and infinite words and over finite trees. Much less is known over infinite trees.