Verification of Parallel Systems via Decomposition

Recently, Milner and Moller have presented several decomposition results for processes. Inspired by these, we investigate decomposition techniques for the verification of parallel systems. In particular, we consider those of the form ‖n i=1 pi = ‖mj=1 qj (I) where pi and qj are (finite) state systems. We provide a decomposition procedure for all pi and qj and give criteria that must be checked on the decomposed processes to see whether (I) does or does not hold. We analyse the complexity of our procedure and show that it is polynomial in n, m and the sizes of pi and qj if there is no communication. We also show that with communication the verification of (I) is co-NP hard, which makes it very unlikely that a polynomial complexity bound exists. But by applying our decomposition technique to Milner’s cyclic scheduler we show that verification can become polynomial in space and time for practical examples, where standard techniques are exponential. Note: The authors are supported by the European Communities under ESPRIT Basic Research Action 3006 (CONCUR). The first author’s current affiliation is University of Utrecht, Department of Philosophy, P.O.Box 80126, 3508 TC Utrecht, email [email protected]. A full version of this paper has also appeared as technical report ECS-LFCS-92-193, Department of Computer Science, University of Edinburgh.