Abstract-Analog and mixed signal (AMS) designs are important integrated circuits that are usually needed at the interface between the electronic system and the real world. Recently, several formal techniques have been introduced for AMS verification. In this paper, we propose a difference equations based bounded model checking approach for AMS systems. We define model checking using a combined system of difference equations for both the analog and digital parts, where the state space exploration algorithm is handled with Taylor approximations over interval domains. We illustrate our approach on the verification of several AMS designs including ∆Σ modulator and oscillator circuits.

Energy efficiency in Wireless Sensor Networks (WSN) is one of the most critical issue regardless of the target application. While scheduling sensors by partitions to preserve energy is a simple and intuitive approach in this context, it is also important to not compromise on the main performance requirements of the considered application. For mission-critical WSN applications, different Quality of Service (QoS) requirements on network performance have to be met. Besides, various assumptions, may effectively impact the sensing performance capabilities of the network. Nevertheless, most analysis techniques focus on the average performance values, and do not consider neither the targeted QoS requirements, nor the probabilistic feature of the algorithm. Based on the theorem proving approach, we first provide, in this paper, an accurate formal analysis of the network lifetime maximization problem, under QoS constraints, for randomlyscheduled wireless sensor networks. After that, we tackle the higher-order-logic formalization of the intrusion coverage intensity, for a modified version of the randomized scheduling, with more realistic assumptions for the intrusion object, in a two or three dimensional plane.