Synthesis of finite state machines for improved state verification

Finite State Machines (FSMs) are used in diverse areas to model hardware and software systems. Verification of FSMs is essential to ensure reliability of systems. To verify that a machine is in an expected state in testing, Unique Input/Output (UIO) sequences are used. The aforementioned testing methodology requires that each state in the FSM has an UIO. However, it is possible for a given machine that few or even none of its states have an UIO sequence. This paper presents a guided heuristic algorithm for synthesizing FSMs such that each state has an UIO sequence. The states of an FSM with identical I/O labels on transitions are grouped in order to identify the states which do not possess UIO sequence. The transitions are then augmented by adding extra output terminals incrementally so that new UIO sequences are created for the states. A greedy approach is used to optimize the number of added outputs. Initially, the transitions which lead to state convergence (i.e., transitions with identical input/output labels taking a set of states to the same next state) and constrained self-loop (i.e., transitions taking a set of states either to itself or leads to state convergence) are identified since a state with only these transitions will never have a UIO sequence. Extra output terminals are added to the FSM which are used only while testing and the augmented output labels make sure that the states are neither convergent nor has constrained self-loop, thereby ensuring UIO sequence. The proposed algorithm, referred to as AUGP, was tested with a large number of FSMs including the Microelectronics Center of North Carolina (MCNC) FSM benchmarks. The augmented state transition table was used as input to a UIO computation algorithm (developed by the same authors [Ahmad I, et al. IEE Proc Comput Digital Tech 2004;151(2):131]) to check the performance of the augmentation algorithm and the tested FSMs were found to possess UIO sequence for all states.