Correctly Slicing Finite State Machines

We consider slicing extended finite state machines. Extended finite state machines (EFSMs) combine a finite state machine with a store and can model a range of computational phenomena, from high-level software to cyberphysical systems. They are essentially interactive and may be nondeterministic so standard techniques for slicing, developed for control flow graphs of programs with a functional semantics, are not immediately applicable. They may be placed in parallel but in this paper we consider them only as stand-alone models. This paper provides the first proofs of correctness for control and data dependence based slicing of EFSMs. We express the semantic correctness of slicing as follows. We demand that the sliced machine simulates the original machine, so an “observable” step taken by the latter can also be done by the former. In the other direction, we cannot hope for a perfect simulation, but demand that for each observable step by the sliced machine, either the original machine simulates it or (i) it gets stuck, or (ii) it loops. To ensure correctness, it suffices to demand that the set of transitions in the slice satisfies two conditions: it must be closed under the well-known notion of data dependence, and it must have the “weak commitment” property highlighted by Danicic et alia If the slice also has the “strong commitment” property, the case (ii) above can be ruled out, meaning that the original machine will simulate the sliced machine except that it may get stuck. We provide statements of correctness for each of the properties “weak commitment” and “strong commitment”. We also give algorithms to compute the least sets satisfying each of the properties “weak commitment” or “strong commitment”.