We propose a new symbolic verification methodology for proving the properties of analog and mixed signal (AMS) designs. Starting with an AMS description and a set of properties and using symbolic computation, we extract a normal mathematical representation for the system in terms of recurrence equations. These normalized equations are used along with an induction verification strategy defined inside the computer algebra system Mathematica to prove the correctness of the properties. We apply our methodology on a third order ∆Σ modulator.

In this paper, we provide a necessary infrastructure to define an abstract state exploration in the HOL theorem prover. Our infrastructure is based on a deep embedding of the Multiway Decision Graphs (MDGs) theory in HOL. MDGs generalize Reduced Ordered Binary Decision Diagrams (ROBDDs) to represent and manipulate a subset of first-order logic formulae. The MDGs embedding is based on the logical formulation of an MDG as Directed Formulae (DF). Then, the MDGs operations are defined and the correctness proof of each operation is provided. The MDG reachability algorithm is then defined as a conversion that uses our MDG theory within HOL. Finally, a set of experimentations over benchmark circuits has been conducted to ensure the applicability and to measure the performance of our approach.

Abstract. In this paper, we show how symbolic algebra in Mathematica can be used to formally verify analog and mixed signal designs. The verification methodology is based on combining induction and constraints solving to generate correctness for the system with respect to given properties. The methodology has the advantage of avoiding exhaustive simulation usually utilized in the verification. We illustrate this methodology by proving the stability of a ΔΣ modulator.

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.