Abstract: Model Based Design approaches for embedded systems aim at generating correct-by-construction control software, guaranteeing that the closed loop system (controller and plant) meets given system level formal specifications. This technical note addresses control synthesis for safety and reachability properties of possibly non-linear discrete time hybrid systems. By means of syntactical transformations that require non-linear terms to be Lipschitz continuous functions, we over-approximate non-linear dynamics with a linear system whose controllers are guaranteed to be controllers of the original system. We evaluate performance of our approach on meaningful control synthesis benchmarks, also comparing it to a state-of-the-art tool.

Abstract: Collagen extracellular matrix is one of the factors related to high passive stiffness of cardiac muscle. However, the architecture and the mechanical aspects of the cardiac collagen matrix are not completely known. In particular, endomysial collagen contribution to the passive mechanics of cardiac muscle as well as its micro anatomical arrangement is still a matter of debate. In order to investigate mechanical and structural properties of endomysial collagen, we consider two alternative computational models of some specific aspects of the cardiac muscle. These two models represent two different views of endomysial collagen distribution: (1) the traditional view and (2) a new view suggested by the data obtained from scanning electron microscopy (SEM) in NaOH macerated samples (a method for isolating collagen from the other tissue). We model the myocardial tissue as a net of spring elements representing the cardiomyocytes together with the endomysial collagen distribution. Each element is a viscous elastic spring, characterized by an elastic and a viscous constant. We connect these springs to imitate the interconnections between collagen fibers. Then we apply to the net of springs some external forces of suitable magnitude and direction, obtaining an extension of the net itself. In our setting, the ratio forces magnitude /net extension is intended to model the stress /strain ratio of a microscopical portion of the myocardial tissue. To solve the problem of the correct identification of the values of the different parameters involved, we use an artificial neural network approach. In particular, we use this technique to learn, given a distribution of external forces, the elastic constants of the springs needed to obtain a desired extension as an equilibrium position. Our experimental findings show that, in the model of collagen distribution structured according to the new view, a given stress /strain ratio (of the net of springs, in the sense specified above) is obtained with much smaller (w.r.t. the other model, corresponding to the traditional view) elasticity constants of the springs. This seems to indicate that by an appropriate structure, a given stiffness of the myocardial tissue can be obtained with endomysial collagen fibers of much smaller size.

Abstract: In this paper we show that statistical properties of the transition graph of a system to be verified can be exploited to improve memory or time performances of verification algorithms. We show experimentally that protocols exhibit transition locality. That is, with respect to levels of a breadth-first state space exploration, state transitions tend to be between states belonging to close levels of the transition graph. We support our claim by measuring transition locality for the set of protocols included in the Mur$\varphi$ verifier distribution. We present a cache-based verification algorithm that exploits transition locality to decrease memory usage and a disk-based verification algorithm that exploits transition locality to decrease disk read accesses, thus reducing the time overhead due to disk usage. Both algorithms have been implemented within the Mur$\varphi$ verifier. Our experimental results show that our cache-based algorithm can typically save more than 40% of memory with an average time penalty of about 50% when using (Mur$\varphi$) bit compression and 100% when using bit compression and hash compaction, whereas our disk-based verification algorithm is typically more than ten times faster than a previously proposed disk-based verification algorithm and, even when using 10% of the memory needed to complete verification, it is only between 40 and 530% (300% on average) slower than (RAM) Mur$\varphi$ with enough memory to complete the verification task at hand. Using just 300 MB of memory our disk-based Mur$\varphi$ was able to complete verification of a protocol with about $10^9$ reachable states. This would require more than 5 GB of memory using standard Mur$\varphi$.