 
Summary: An Iterative Method for Reached State Approximation
Cliff Cordeiro
Abstract
In this paper we present a new method for computing the approximate reached state set of a finite state machine by
modifying its transition relation. Both upper and lower bounds are computed using this method.
1 Introduction
Computing the set of reached states in a finite state machine (FSM) is a key operation in both verification [1] and synthesis
[2] & [3]. The reached state set allows designers to check a design for errors and other unwanted behavior. It is a precise
measure of the exact set of states a design can take under all possible inputs.
Given a directed graph, and a set of initial nodes in the graph, reachability computes the set of nodes on some path from
the initial nodes. A FSM can be represented by a directed graph, which is also called a state transition graph. Computing the
reachable states (nodes) of this graph can be done by a breadth first search traversal of the state transition graph beginning at
the initial states.
Unfortunately this computation explodes when the number of states in the FSM becomes very large, as is the case in real
designs. This is often called the state explosion problem. To attempt to overcome this problem, an implicit representation
called a binary decision diagram or BDD [4], is used to represent the required quantities. e.g. the transition relation (TR),
which implicitly represents the FSM's state transition graph, and the initial and reachable sets of states.
In order to further combat the state explosion problem, we propose to perform modifications on the transition relation
before computing the reached state set. This will have the effect of simplifying the computation while introducing some error.
By limiting the types of modifications to the TR, we can assure that the value returned by the reachability computation is
