Abstract: Many software as well digital hardware automatic synthesis methods define the set of implementations meeting the given system specifications with a boolean relation K. In such a context a fundamental step in the software (hardware) synthesis process is finding effective solutions to the functional equation defined by K. This entails finding a (set of) boolean function(s) F (typically represented using OBDDs, Ordered Binary Decision Diagrams) such that: 1) for all x for which K is satisfiable, K(x, F(x)) = 1 holds; 2) the implementation of F is efficient with respect to given implementation parameters such as code size or execution time. While this problem has been widely studied in digital hardware synthesis, little has been done in a software synthesis context. Unfortunately the approaches developed for hardware synthesis cannot be directly used in a software context. This motivates investigation of effective methods to solve the above problem when F has to be implemented with software. In this paper we present an algorithm that, from an OBDD representation for K, generates a C code implementation for F that has the same size as the OBDD for F and a WCET (Worst Case Execution Time) at most O(nr), being n = |x| the number of arguments of functions in F and r the number of functions in F.

Abstract: Many Embedded Systems are indeed Software Based Control Systems, that is control systems whose controller consists of control software running on a microcontroller device. This motivates investigation on Formal Model Based Design approaches for automatic synthesis of embedded systems control software.
We present an algorithm, along with a tool QKS implementing it, that from a formal model (as a Discrete Time Linear Hybrid System) of the controlled system (plant), implementation specifications (that is, number of bits in the Analog-to-Digital, AD, conversion) and System Level Formal Specifications (that is, safety and liveness requirements for the closed loop system) returns correct-by-construction control software that has a Worst Case Execution Time (WCET) linear in the number of AD bits and meets the given specifications.
We show feasibility of our approach by presenting experimental results on using it to synthesize control software for a buck DC-DC converter, a widely used mixed-mode analog circuit, and for the inverted pendulum.

Abstract: Fuzzy control is well known as a powerful technique for designing and realizing control systems. However, statistical evidence for their correct behavior may be not enough, even when it is based on a large number of samplings. In order to provide a more systematic verification process, the cell-to-cell mapping technology has been used in a number of cases as a verification tool for fuzzy control systems and, more recently, to assess their optimality and robustness. However, cell-to-cell mapping is typically limited in the number of cells it can explore. To overcome this limitation, in this paper we show how model checking techniques may be instead used to verify the correct behavior of a fuzzy control system. To this end, we use a modified version of theMurphi verifier, which ease the modeling phase by allowing to use finite precision real numbers and external C functions. In this way, also already designed simulators may be used for the verification phase. With respect to the cell mapping technique, our approach appears to be complementary; indeed, it explores a much larger number of states, at the cost of being less informative on the global dynamic of the system.

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.