Thread-modular verification is Cartesian abstract interpretation

Abstract. Verification of multithreaded programs is difficult. It requires reasoning about state spaces that grow exponentially in the number of concurrent threads. Successful verification techniques based on modular composition of overapproximations of thread behaviors have been de-signed for this task. These techniques have been traditionally described in assume-guarantee style, which does not admit reasoning about the ab-straction properties of the involved compositional argument. Flanagan and Qadeer thread-modular algorithm is a characteristic representative of such techniques. In this paper, we investigate the formalization of this algorithm in the framework of abstract interpretation. We identify the abstraction that the algorithm implements; its definition involves Cartesian products of sets. Our result provides a basis for the system-atic study of similar abstractions for dealing with the state explosion problem. As a first step in this direction, we obtain polynomial-time al-gorithms based on Cartesian abstraction that enjoy increased precision with respect to the Flanagan-Qadeer method. We limit the design space for future polynomial-time algorithms by providing a characterization of minimal precision increase that leads to loss of polynomial-time com-plexity.