Given a sequential resource allocation system (RAS) topology structure, a state space, called an impulse state space, corresponding to the impulse response of a linear time-invariant system (LTS), is computed by small enough configuration of the considered RAS. Given an initial resource configuration of a RAS which corresponds to an input of an LTS, a complete state enumeration can be obtained by defining the convolution of this configuration with the pre-computed impulse state space. One example embodiment reduces central processing unit (CPU) time to process instructions that compute a target state space of a RAS includes constructing an initial RAS and an initial state space, and extending the initial state space iteratively under a target resource configuration.