Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)We present a generalized test case generation method, called the G method. Although inspired by the W method, the G method, in contrast, allows for test case suite generation even in the absence of characterization sets for the specification models. Instead, the G method relies on knowledge about the index of certain equivalences induced at the implementation models. We show that the W method can be derived from the G method as a particular case. Moreover, we discuss some naturally occurring infinite classes of FSM models over which the G method generates test suites that are exponentially more compact than those produced by the W method.231147172Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)