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In this paper, we propose a global assignment theory for “encoding” state graph transformations. A constraint satisfaction framework is proposed that can guarantee necessary and sufficient conditions for a state graph assignment to result in a transformed state graph that is race-free. 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 l-safe net into a correct a-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.

A generalized state assignment theory for transformation on signal transition graphs