Abstract: To support Model Based Design of Cyber-Physical Systems (CPSs) many simulation based approaches to System Level Formal Verification (SLFV) have been devised. Basically, these are Bounded Model Checking approaches (since simulation horizon is of course bounded) relying on simulators to compute the system dynamics and thereby verify the given system properties. The main obstacle to simulation based SLFV is the large number of simulation scenarios to be considered and thus the huge amount of simulation time needed to complete the verification task. To save on computation time, simulation based SLFV approaches exploit the capability of simulators to save and restore simulation states. Essentially, such a time saving is obtained by optimising the simulation script defining the simulation activity needed to carry out the verification task. Although such approaches aim to (bounded) formal verification, as a matter of fact, the proof of correctness of the methods to optimise simulation scripts basically relies on an intuitive semantics for simulation scripting languages. This hampers the possibility of formally showing that the optimisations introduced to speed up the simulation activity do not actually omit checking of relevant behaviours for the system under verification. The aim of this paper is to fill the above gap by presenting an operational semantics for simulation scripting languages and by proving soundness and completeness properties for it. This, in turn, enables formal proofs of equivalence between unoptimised and optimised simulation scripts.

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: 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: 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) linear in nr, being n = |x| the number of input arguments for functions in F and r the number of functions in F.