Minimizing Characterizing Sets

A characterizing set (CS) for a given finite state machine (FSM) defines a set of input sequences such that for any pair of states of FSM, there exists an input sequence in a CS that can separate these states. There are techniques that generate test sequences with guaranteed fault detection power using CSs. The number of inputs and input sequences in a CS directly impacts the cost of the test: the higher the number of elements, the longer it takes to generate the test. Despite the direct benefits of using CSs with fewer sequences, there has been no work focused on generating minimum sized characterizing sets. In this paper, we show that constructing CS with fewer elements is a PSPACE-Hard problem and that the corresponding decision problem is PSPACE-Complete. We then introduce a heuristic to construct CSs with fewer input sequences. We evaluate the proposed algorithm using randomly generated FSMs as well as some benchmark FSMs. The results are promising, and the proposed method reduces the number of test sequences by 37.3% and decreases the total length of the tests by 34.6% on the average.