In this paper we generalize a framework previously presented for the analysis of dyadic cooperation of finite state machines (FSM) performing code acquisition. Our aim is to tackle the limitations of this framework making it more general, and suitable for larger range of applications. Moreover, we introduce in our paper new Bidirectional (BD) cooperation strategies to exchange information among FSMs. Although some of these strategies require the machines to work in parallel, we managed to present an analytical framework to analyze their performances based on flowgraphs. Using this technique, we arrived at closed forms of the Mean Acquisition Time (MAT) which we used as an assessment method to test the performances of the cooperation strategies on a case study of dual band Galileo receivers. Numerical results demonstrate the superiority of the suggested cooperation architectures over the conventional segregated approaches when code acquisition is concerned. The generality of our framework makes it appropriate to study and analyze many other applications.