Manipulations of FSMs Represented as Sequential Circuits

Abstract

In many cases, hard computational problems can be reformulated using decomposition and partitioning, which can lead to computational advantages. An example is image computation, which is a core computation in formal verification. In its simplest form, the image of a set of states is computed using the formula:

$$\begin{array}{rcl} Img(ns) = {\exists }_{i,cs}\ [T(i,cs,ns)\,.\,\xi (cs)],& & \\ \end{array}$$

where T(i, cs, ns) is the transition relation, ξ(cs) is the set of current states, i is the set of input variables, and cs(ns) is the set of current (next) state variables. The image, Img(ns), is the set of states reachable in one transition under all possible inputs from the current states, ξ(cs), using the state transition structure given by T(i, cs, ns).