Minimizing Characterizing sets

Abstract

• Provides an algorithm that generates compact Characterizing sets from deterministic FSMs . • Shows that constructing minimum sized Characterising sets is PSPACE complete for deterministic FSMs . • Shows that constructing Characterising sets with minimum total number of inputs is NP Complete for deterministic FSMs . • Presents the results of a set of experiment and discussions in a rigorous way. A characterizing set (CS) for a deterministic finite state machine (FSM) M is a set of input sequences that, between them, separate (distinguish) all of the states of M . CSs are used within several test generation techniques that return test suites with guaranteed fault detection power. The number of input sequences in a CS directly affects the cost of applying the resultant test suite. In this paper, we study the complexity of decision problems associated with deriving a smallest CS from an FSM, showing that checking the existence of a CS with K sequences is PSPACE-complete . We also consider the length of a CS, which is the sum of the lengths of the input sequences in the CS. It transpires that the problem of deciding whether there is a CS with length at most K is NP-complete . Motivated by these results, we introduce a heuristic to construct a CS, from a deterministic FSM, with the aim of minimizing the number of input sequences. We evaluated the proposed algorithm by assessing its effect when used within a classical test generation algorithm (the W-method). In the evaluation, we used both randomly generated FSMs and benchmark FSMs. The results are promising, with the proposed algorithm reducing the number of test sequences by 37.3% and decreasing the total length of the test suites by 34.6% on average.