The trace equivalence of BPP was shown to be undecidable by Hirshfeld. We show that the trace equivalence remains undecidable even if the number of labels is restricted to two. The undecidability result holds also for the simulation of two-label BPP processes. These results imply undecidability of some behavioral type systems for the π-calculus.

On the one hand, the inclusion problem for nonerasing and erasing pattern languages is undecidable; see JSSY95]. On the other hand, the language equivalence problem for NE-pattern languages is trivially decidable (see Ang80a]) but the question of whether the same holds for E-pattern languages is still open. It has been conjectured by Jiang et al. JSSY95] that the language equivalence problem fo...