Equivalence checking for weak bi-Kleene algebra

Pomset automata are an operational model of weak bi-Kleene algebra, which describes programs that can fork execution into parallel threads, upon completion join to resume as a single thread. We characterize fragment pomset admits decision procedure for language equivalence. Furthermore, we prove this corresponds precisely series-rational expressions, i.e., rational expressions with additional operator bounded parallelism. As consequence, obtain new proof equivalence is decidable.