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: In today’s competitive market designing of digital systems (hardware as well as software) faces tremendous challenges. In fact, notwithstanding an ever decreasing project budget, time to market and product lifetime, designers are faced with an ever increasing system complexity and customer expected quality. The above situation calls for better and better formal verification techniques at all steps of the design flow. This special issue is devoted to publishing revised versions of contributions first presented at the 12th Advanced Research Working Conference on Correct Hardware Design and Verification Methods (CHARME) held 21–24 October 2003 in L’Aquila, Italy. Authors of well regarded papers from CHARME’03 were invited to submit to this special issue. All papers included here have been suitably extended and have undergone an independent round of reviewing.

Abstract: In this paper we present an explicit disk-based verification algorithm for Probabilistic Systems defining discrete time/finite state Markov Chains. Given a Markov Chain and an integer k (horizon), our algorithm checks whether the probability of reaching an error state in at most k steps is below a given threshold. We present an implementation of our algorithm within a suitable extension of the Mur$\varphi$ verifier. We call the resulting probabilistic model checker FHP-Mur$\varphi$ (Finite Horizon Probabilistic Mur$\varphi$). We present experimental results comparing FHP-Mur$\varphi$ with (a finite horizon subset of) PRISM, a state-of-the-art symbolic model checker for Markov Chains. Our experimental results show that FHP-Mur$\varphi$ can handle systems that are out of reach for PRISM, namely those involving arithmetic operations on the state variables (e.g. hybrid systems).

Abstract: Model checking of safety properties can be scaled up by pooling the CPU and memory resources of multiple computers. As compute clusters containing 100s of nodes, with each node realized using multi-core (e.g., 2) CPUs will be widespread, a model checker based on the parallel (shared memory) and distributed (message passing) paradigms will more efficiently use the hardware resources. Such a model checker can be designed by having each node employ two shared memory threads that run on the (typically) two CPUs of a node, with one thread responsible for state generation, and the other for efficient communication, including (i) performing overlapped asynchronous message passing, and (ii) aggregating the states to be sent into larger chunks in order to improve communication network utilization. We present the design details of such a novel model checking architecture called Eddy. We describe the design rationale, details of how the threads interact and yield control, exchange messages, as well as detect termination. We have realized an instance of this architecture for the Murphi modeling language. Called Eddy_Murphi, we report its performance over the number of nodes as well as communication parameters such as those controlling state aggregation. Nearly linear reduction of compute time with increasing number of nodes is observed. Our thread task partition is done in such a way that it is modular, easy to port across different modeling languages, and easy to tune across a variety of platforms.