Order-independence of vector-based transition systems

Semantics of many specification languages, particularly those used in the domain of hardware, is described in terms of vector-based transition systems. In such a transition system, each macro-step transition is labeled by a vector of inputs. When performing a macro-step, several inputs may potentially change. Each macro-step can thus be decomposed in a number of micro-steps, taking one input change at a time into account. This is akin to an interleaving semantics, where a concurrent step is represented by an interleaving of its constituting components. We present criteria on vector-based transition systems, which guarantee that the next state computation is independent of the order in which these micro-steps are executed. If our criteria are satisfied by the semantic definition of a certain specification, then its state-space generation or exploration algorithm needs to only consider one representative among all possible permutations of such micro-steps. We demonstrate the applicability of our criteria to the specification of transistor netlists.