Finite-state concurrent programs can be expressed pairwise

We present a \emph{pairwise normal form} for finite-state shared memory concurrent programs: all variables are shared between exactly two processes, and the guards on transitions are conjunctions of conditions over this pairwise shared state. This representation has been used to efficiently (in polynomial time) synthesize and model-check correctness properties of concurrent programs. Our main result is that any finite state concurrent program can be transformed into pairwise normal form. Specifically, if $Q$ is an arbitrary finite-state shared memory concurrent program, then there exists a finite-state shared memory concurrent program $P$ expressed in pairwise normal form such that $P$ is strongly bisimilar to $Q$. Our result is constructive: we give an algorithm for producing $P$, given $Q$.