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