  Symbolic controller synthesis is a fully-automated and correct-by-design
synthesis scheme whose limitations are its immense memory and runtime
requirements. A current trend to compensate for this downside is to develop
techniques for parallel execution of the scheme both in mathematical foundation
and in software implementation. In this paper we present a generalized
Bellman-Ford algorithm to be used in the so-called symbolic optimal control,
which is an extension of the aforementioned synthesis scheme. Compared to the
widely used Dijkstra algorithm our algorithm has two advantages. It allows for
cost functions taking arbitrary (e.g. negative) values and for parallel
execution with the ability for trading processing speed for memory consumption.
We motivate the usefulness of negative cost values on a scenario of aerial
firefighting with unmanned aerial vehicles. In addition, this four-dimensional
numerical example, which is rich in detail, demonstrates the great performance
of our algorithm.
