A system and method for analyzing concurrent programs that guarantees optimality in the number of thread inter-leavings to be explored. Optimality is ensured by globally constraining the inter-leavings of the local operations of its threads so that only quasi-monotonic sequences of threads operations are explored. For efficiency, a SAT/SMT solver is used to explore the quasi-monotonic computations of the given concurrent program. Constraints are added dynamically during exploration of the concurrent program via a SAT/SMT solver to ensure quasi-montonicity for model checking.