Message sequence charts are a widely used notation to express requirements specifications of multi-agent systems. The semantics of message sequence charts can be defined algebraically in the theory of agents and insertion functions. Using this algebra, one can split message sequence chart scenarios into sets of Hoare triples consisting of precondition, the specification of a finite process, and a postcondition. We refer to such triples as "basic protocols." In this paper, we discuss tools to prove properties of systems described as basic protocols, such as the completeness (at each of its stages the system behavior has a possible continuation) and consistency (at each stage the system behavior is deterministic) of the specification, or the correspondence of the specified behavior to given scenarios. Together, these tools constitute a powerful environment for the formal verification of requirements specifications expressed through message sequence charts. *

SUMMARY Mechanisms of stress transfer and probabilistic models have been widely investigated to explain earthquake clustering features. However, these approaches are still far from being able to link individual events and to determine the number of earthquakes caused by a single event. An alternative approach based on proximity functions allows us to generate hierarchical clustering trees and to identify pairs of nearest-neighbours between consecutive levels of hierarchy. Then, the productivity of an earthquake is the number of events of the next level to which it is linked. Using a relative magnitude threshold ΔM to account for scale invariance in the triggering process, we show that the ΔM-productivity attached to each event is a random variable that follows an exponential distribution. The exponential rate of this distribution does not depend on the magnitude of triggering events and systematically decreases with depth. These results could now be used to characterize active fault systems and improve epidemic models of seismicity.

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