Methods and apparatus are provided for exploring paths through a graph representation of a program or another entity. According to one aspect of the invention, at least one property of a state machine, such as a graph representing a software program, is evaluated. One or more paths in the state machine are evaluated using a state exploration algorithm, wherein the state exploration algorithm maintains a stack data structure representing a current path being processed from an entry state to a current state and a visited state cache indicating zero or more states that have been evaluated. When a state satisfies at least one property, such as having an error, each of the states in the path are removed from the visited states cache if the path satisfies one or more predefined criteria. The one or more predefined criteria may comprise a feasibility of the path.