Minimum-cost solutions for testing protocols with timers

A method to generate a minimum-cost test sequence for a protocol with timers is presented. The protocol timers limit the number of consecutive self-loops that can be realized in a given state. The solution presented is applicable to test sequences that use any state identification method such as UIO sequences, distinguishing sequences, and characterizing sequences. If valid and inopportune transition testing are combined, or if only valid transitions are considered, a minimum-cost solution exists. In the case of testing inopportune transitions separately, however, finding a minimum-cost solution is shown to be NP-hard.