Best Fairness Hierarchy in Elementary Nets

The fairness hierarchy and conspiracies, the notions introduced by Best, are studied in the context of elementary nets. Proving that sequential as well as persistent systems are conspiracy-free, we indicate two main roots of conspiracies: distributed memory and conflicts. Using the notion of marking-fairness, due to Merceron, we prove that T0-fairness + M0-fairness = T∞-fairness. This result gives a method of a local control ensuring globally fair executions. Next we show how to check, if a given elementary net is conspiracy-free, and prove the obtained criterion to be effectively decidable. Finally, we give a characterization of live concurrent systems, using the notion of ∞ -fairness.