Extracting State Transition Models from i* Models

i* models are inherently sequence agnostic. There is an immediate need to bridge the gap between such a sequence agnostic model and an industry implemented process modelling standard like Business Process Modelling Notation (BPMN). This work is an attempt to build State Transition Models from i* models. In this paper, we first spell out the Naive Algorithm formally, which is on the lines of Formal Tropos. We demonstrate how the growth of the State Transition Model Space can be mapped to the problem of finding the number of possible paths between the Least Upper Bound (LUB) and the Greatest Lower Bound (GLB) of a k-dimensional hypercube Lattice structure. We formally present the mathematics for doing a quantitative analysis of the space growth. The Naive Algorithm has its main drawback in the hyperexponential explosion caused in the State Transition Model space. This is identified and the Semantic Implosion Algorithm is proposed which exploits the temporal information embedded within the i* model of an enterprise to reduce the rate of growth of the State Transition Model space. A comparative quantitative analysis between the two approaches concludes the superiority of the Semantic Implosion Algorithm.