Deriving tests for the synchronous composition of deterministic complete Finite State Machines

Abstract

The paper is devoted to deriving tests with guaranteed fault coverage for Finite State Machines (FSM). FSMs and their compositions are widely used when deriving tests for various systems, including interactive services, and the synchronous composition describes the behavior of a multi modular system when all the channels are active at each time instance. Without loss of generality, we assume that an output port of each FSM component is connected with at most one input port of another FSM component and propose a simplified approach for deriving the synchronous composition of deterministic complete FSMs using well known operators over FSMs. We also extend the sufficient conditions for checking the closure of the synchronous composition operator with respect to deterministic complete FSMs showing that for the operator closure it is sufficient that each composition cycle contains a Moore pair, i.e., a pair <input port, output port> of some component FSM such that outputs do not significantly depend on inputs (Moore condition). If a system under test has the same structure as the reference composition and faults of component FSMs do not break the Moore condition, then a transition tour of the composed FSM is a good quality test when component states can be observed (testing with open state). We also propose how to derive a test with guaranteed fault coverage for a component FSM of our interest when states cannot be observed under the condition that input and output ports of a component under test can still be observed.