Branch-Well-Structured Transition Systems and Extensions

We propose a relaxation to the definition of a well-structured transition systems (WSTS) while retaining the decidability of boundedness and termination. In this class, we ease the well-quasi-ordered (wqo) condition to be applicable only between states that are reachable one from another. Furthermore, we also relax the monotony condition in the same way. While this retains the decidability of termination and boundedness, it appears that the coverability problem is undecidable. To this end, we define a new notion of monotony, called cover-monotony, which is strictly more general than the usual monotony and still allows to decide a restricted form of the coverability problem.