Distinguing Non-deterministic Timed Finite State Machines

Abstract

Abstract. Conformance testing with the guaranteed fault coverage is based on distinguishing faulty system implementations from the corresponding system specification. We consider timed systems modeled by timed possibly nondeterministic finite state machines (TFSMs) and propose algorithms for distinguishing two TFSMs. In particular, we present a preset algorithm for separating two separable TFSMs and an adaptive algorithm for r-distinguishing two possibly non-separable TFSMs. The proposed techniques extend existing methods for untimed non-deterministic FSMs by dealing with the fact that unlike untimed FSMs in general, a TFSM has an infinite number of timed inputs. Correspondingly we state that the upper bounds on the length of distinguishing sequences are the same as for untimed FSMs.

Distinguishing Experiments for Timed Nondeterministic Finite State Machines

“…This paper extends a related preliminary work in [6] to TFSMs which can have non-zero output delays. Moreover, the presented work provides a simpler strategy for deriving distinguishing experiments.…”

“…Hierons et al [8] introduce a timed stochastic FSM model. Gromov et al [6] consider a timed complete nondeterministic FSM model where transitions are guarded by time constraints over a single clock. The clock is reset at the execution of a transition.…”

“…The clock is reset at the execution of a transition. In this paper, we consider a model similar to that in [6], yet extended to deal with non-zero output delays sometimes called output timeouts. The considered model can be regarded as a temporal extension of FSMs where a transition is fired only if a given input is given in time (bounded by given lower and upper bounds) that is counted from the moment when a current state is reached.…”

“…Moreover, the presented work provides a simpler strategy for deriving distinguishing experiments. In particular, in [6] two TFSMs are distinguished based on their intersection using more complex algorithms that inherit ideas from traditional untimed FSM methods mixed with the derivation of appropriate partitions of input domains for handling time constraints. The strategy proposed in this paper is based on a corresponding (untimed) FSM abstraction of the intersection of two TFSMs and this allows simpler adaptation of existing traditional FSM-based methods for distinguishing TFSMs.…”

Detecting Faults in TFTP Implementations using Finite State Machines with Timeouts

“…Some of them use FSM-based strategies for test derivation [4][5][6][7][8][9][10][11]. One of such strategies uses the model of a timed FSM (TFSM) with so-called timeouts [7][8][9][10][11], i.e., if no input is applied during an appropriate time period the FSM can move to another prescribed state. Correspondingly, the behavior of an FMS significantly depends on a time instance when an input is applied, i.e., the behavior of the FSM is specified for timed input sequences.…”