Timed Testing under Partial Observability

This paper studies the problem of model-based testing of real-time systems that are only partially observable. We model the System Under Test (SUT) using Timed Game Automata (TGA) which has internal actions, uncontrollable outputs and timing uncertainty of outputs. We define the partial observability of SUT using a set of predicates over the TGA state space, and specify the test purposes in Computation Tree Logic (CTL) formulas. A recently developed partially observable timed game solver is used to generate winning strategies, which are used as test cases. We propose a conformance testing framework, define a partial observation-based conformance relation, present the test execution algorithms, and prove the soundness and completeness of this test method (i.e., a detected error really violates the conformance relation; and if the SUT violates the test purpose, then a test case can be generated to detect this violation). Experiments on some non-trivial examples show that this method yields encouraging results.