Identical tasks and counter variables in an integer programming-based approach to verification

Analysis of concurrent systems is plagued by the state explosion problem. The constrained expression analysis technique uses necessary conditions, in the form of linear inequalities, to verify certain properties of concurrent systems without enumerating the system's states. While effective against the state explosion due to interleaving, the technique fails to yield a tractable analysis if the size of the components themselves grow exponentially due to the use of variables in the components. As a partial solution to this problem, we present a technique for representing certain program variables as integer programming variables. We also present a synergistic technique for efficiently representing many identical components in the context of an integer programming analysis.<>