Equation-based modelling is a powerful approach to tame the complexity of large-scale simulation problems. Equation-based tools automatically translate models into imperative languages. When confronted with nowadays’ problems, however, well assessed model translation techniques exhibit scalability issues that are particularly severe when models contain very large arrays. In fact, such models can be made very compact by enclosing equations into looping constructs, but reflecting the same compactness into the translated imperative code is nontrivial. In this paper, we face this issue by concentrating on a key step of equations-to-code translation, the equation/variable matching. We first show that an efficient translation of models with (large) arrays needs awareness of their presence, by defining a figure of merit to measure how much the looping constructs are preserved along the translation. We then show that the said figure of merit allows to define an optimal array-aware matching, and as our main result, that the so stated optimal array-aware matching problem is NP-complete. As an additional result, we propose a heuristic algorithm capable of performing array-aware matching in polynomial time. The proposed algorithm can be proficiently used by model translator developers in the implementation of efficient tools for large-scale system simulation.

Clock synchronization is a necessary component in modern distributed systems, especially Wireless Sensor Networks (WSNs). Despite the great effort and the numerous improvements, the existing synchronization schemes do not yet address the cancellation of propagation delays. Up to a few years ago, this was not perceived as a problem, because the time-stamping precision was a more limiting factor for the accuracy achievable with a synchronization scheme. However, the recent introduction of efficient flooding schemes based on constructive interference has greatly improved the achievable accuracy, to the point where propagation delays can effectively become the main source of error. In this paper, we propose a method to estimate and compensate for the network propagation delays. Our proposal does not require to maintain a spanning tree of the network, and exploits constructive interference even to transmit packets whose content are slightly different. To show the validity of the approach, we implemented the propagation delay estimator on top of the FLOPSYNC-2 synchronization scheme. Experimental results prove the feasibility of measuring propagation delays using off-the-shelf microcontrollers and radio transceivers, and show how the proposed solution allows to achieve sub-microsecond clock synchronization even for networks where propagation delays are significant.