A generalized state assignment theory for transformations on signal transition graphs

Abstract

In this article, we propose a global assignment theory forencoding state graph transformations. A constraint satisfaction framework is proposed that can guaranteenecessary and sufficient conditions for a state graph assignment to result in a transformed state graph that is free of critical races. Performing transformations at the state graph level has the advantage that the requirements imposed on the initial STG are very weak. Unlike previous methods, the initial STG need not be a live, safe, nor a free choice net. The only requirement is that the corresponding initial state graph is finite, connected, and has a consistent state assignment. Hence, a very broad range of signal transition graphs can be synthesized. The transformations achievable using the proposed framework correspond to very complex transformations on signal transition graphs. Even transformations that convert a free choice net into a correct non-free choice net and a 1-safe net into a correct 2-safe net are feasible. Addition of transitions that do not follow the Petri net firing rule is also possible. Even though our method can search a large solution space, we will show that it is possible to solve the problem in an exact way in acceptable CPU times in many practical cases.