Strong Bisimilarity and Regularity of Basic Parallel Processes Is PSPACE-Hard

We show that the problem of checking whether two processes definable in the syntax of Basic Parallel Processes (BPP) are strongly bisimilar is PSPACE-hard. We also demonstrate that there is a polynomial time reduction from the strong bisimilarity checking problem of regular BPP to the strong regularity (finiteness) checking of BPP. This implies that strong regularity of BPP is also PSPACE-hard.