Optimal Test Input Sequence Generation for Finite State Models and Pushdown Systems

Finite state machines and pushdown systems are frequently used in model based testing. In such testing, the system under test is abstractly modeled as a finite state machine having a finite set of states and a labeled transition relation between the states. A pushdown system, additionally, has an unbounded stack. Test inputs are then generated by enumerating a set of sequences of transitions labels from the model. There has been a lot of research that focussed on generation of test input sequences satisfying various coverage criteria. In this paper, we consider the problem of generating a set of test input sequences that satisfy certain coverage criteria -- cover all transition labels or cover all length-$n$ transition label sequences at least once -- while minimizing the sum of the length of the sequences in the set. We show that these optimal test input generation problems can be reduced to integer linear programming (ILP) problems. We also prove that our optimal test input generation problems are NP-Complete. We report our experimental results on a prototype implementation for finite states machines.