Using minimal minterms to represent programmability

We address the problem of formally representing the programmability of a system. We define the programmability of a system as the set of valid execution paths that can be configured statically by software. We formally represent this programmability as a Boolean function. From this representation, we extract a subset of on-set minterms that we call minimal minterms. We prove that these minimal minterms represent the set of smallest schedulable atomic actions of the system, and that we can use a special generator relation to determine if subsets of these actions can be executed in parallel. We also prove that given an arbitrary Boolean function we can extract the minimal minterms and recreate the entire on-set by applying the generator relation to every element of the power set of the set of minimal minterms. Thus, the minimal minterms represent the complete instruction set supported by the system, and the generator relation represents the inherent parallelism among the instructions. Furthermore, we automatically generate the required software development tools and hardware implementation from this representation of programmability. Finally, we show that we can efficiently compute the minimal minterms and apply the generator relation to verify parallel executions on interesting data path systems.