How to parallelize sequential processes

Abstract

A process is prime if it cannot be decomposed into a parallel product of nontrivial processes. We characterize all non-prime normed BPA processes together with their decompositions by means of normal forms which are designed in this paper. Using this result we demonstrate decidability of the problem whether a given normed BPA process is prime; moreover, we show that non-prime normed BPA processes can be decomposed into primes effectively. This brings other positive decidability results. Finally, we prove that bisimilarity is decidable in a large subclass of normed PA processes.