Carna Radojicic

Embedded tutorial: Analog-/mixed-signal verification methods for AMS coverage analysis

Analog-/Mixed-Signal (AMS) design verification is one of the most challenging and time consuming tasks of todays complex system on chip (SoC) designs. In contrast to digital system design, AMS designers have to deal with a continuous state space of conservative quantities, highly nonlinear relationships, non-functional influences, etc. enlarging the number of possibly critical scenarios to infinity. In this special session we demonstrate the verification of functional properties using simulative and formal methods. We combine different approaches including automated abstraction and refinement of mixed-level models, state-space discretization as well as affine arithmetic. To reach sufficient verification coverage with reasonable time and effort, we use enhanced simulation schemes to avoid conventional simulation drawbacks.

Formal verification of mixed-signal designs using extended affine arithmetic

The complexity and heterogeneity of todays mixed-signal systems makes verification a challenge. A particular challenge is the sensitivity of analog parts to variations in parameters, inputs, or initial conditions. We present a methodology for formal verification of mixed-signal systems that verifies the impact of variations of parameters, inputs, or initial conditions on specified properties. Compared with state of the art, the proposed methodology can be integrated easily in existing design flows, handles analog and digital parts, and offers improved scalability. The method is applied on a third order ΣΔ Modulator for verifying the stability property. The results show that our approach is using one simulation run able to find the input sequence that could lead to the undesired system behavior. These values are often not trivial and most likely would never be detected by traditional simulation-based techniques.

Verification of mixed-signal systems with affine arithmetic assertions

Embedded systems include an increasing share of analog/mixed-signal components that are tightly interwoven with functionality of digital HW/SW systems. A challenge for verification is that even small deviations in analog components can lead to significant changes in system properties. In this paper we propose the combination of range-based, semisymbolic simulation with assertion checking. We show that this approach combines advantages, but as well some limitations, of multirun simulations with formal techniques. The efficiency of the proposed method is demonstrated by several examples.

Towards Verification of Uncertain Cyber-Physical Systems.

Cyber-Physical Systems (CPS) pose new challenges to verification and validation that go beyond the proof of functional correctness based on high-level models. Particular challenges are, in particular for formal methods, its heterogeneity and scalability. For numerical simulation, uncertain behavior can hardly be covered in a comprehensive way which motivates the use of symbolic methods. The paper describes an approach for symbolic simulation-based verification of CPS with uncertainties. We define a symbolic model and representation of uncertain computations: Affine Arithmetic Decision Diagrams. Then we integrate this approach in the SystemC AMS simulator that supports simulation in different models of computation. We demonstrate the approach by analyzing a water-level monitor with uncertainties, self-diagnosis, and error-reactions.

Novel metrics for Analog Mixed-Signal coverage

On the contrary to the digital world, no coverage definition exists in the Analog/Mixed-Signal (AMS) context. As digital coverage helps digital designers and verification engineers to evaluate their verification progress, analog designers do not have such metrics. This paper proposes a set of different analog coverage metrics, which improve the confidence in AMS circuit verification. We will demonstrate, that no single overall coverage metric exists. However, as with digital coverage, the proposed analog coverage metrics could substantially help in rating the verification process. Illustrated by a complex AMS circuit example we will explore the limits of analog coverage methodologies as well as the benefits on different levels of abstraction ranging from transistor level up to system level.

Towards formal validation: Symbolic simulation of SystemC models

With increasing complexity of systems, specifications are becoming more and more comprehensive and often inconsistent or incomplete. To validate a system regarding realistic use cases, systems are simulated “in the loop”, including the application and usage scenarios. This paper describes a first approach to analyze software systems “in the loop” in a more comprehensive way by symbolic simulation. For this purpose we propose a new approach to separate modeling- and implementation languages from formal methods. For demonstration, we implemented it in the SYCYPHOS framework based on C++ and SystemC AMS.

System refinement design flow based on semi-symbolic simulations

Range based system simulations are increasingly preferred in recent years to cope with the performance issues inherent with standard multi-run simulations. Traditionally, deviations of nominal system parameters are considered statistically by steadily varying the system parameters and simulating all of these parameter space realizations in multiple simulation runs. In range based or semi-symbolic simulations, deviations of system parameters are modeled in continuous ranges expressed as symbolic quantities. Therefore, a range based system simulation achieves in one simulation run the result for all the modeled parameter deviations, thus significantly reducing the computation effort. This work uses a semi-symbolic simulation environment to obtain a range based system response. Subsequently the symbolic labeling of ranges is used to trace back the resulting sub-ranges of the system response to their respective parameter origin to identify potential refinement candidates. Based on this capability a refinement design flow is introduced which allows by refinements to improve the robustness and accuracy of cyber physical systems. Identifying refinement candidates is manifold and is demonstrated in an example by assessing a communication receiver SNR metric.

Semi-symbolic analysis of mixed-signal systems including discontinuities

The paper describes an approach for semi-symbolic analysis of mixed-signal systems that contain discontinuous functions, e.g. due to modeling comparators. For modeling and semi-symbolic simulation, we use extended Affine Arithmetic. Affine Arithmetic is currently limited to accurate analysis of linear functions and mild non-linear functions, but not yet discontinuities. In this paper we extend the approach to also handle discontinuities. For demonstration, we symbolically analyze a ΣΔ-modulator.

On more dependable assertion-based verification

The increased design complexity of analog/mixed signal (AMS) systems puts a high pressure on researchers to find the efficient solutions for the verification of these systems. In contrast to digital designs, the nonlinear nature and higher sensitivity of AMS systems to parameter variations make the verification process more difficult. The focus of this paper is the verification of system robustness with respect to frequency and phase properties. For this purpose, the method, which combines simulation with assertion-based approach, is used. Assertions describing desired system properties use simulation results to verify the system behaviour. In order to provide more formal results using simulation-based methods, deviations of system parameters are modeled as ranges and superimposed to the nominal design model. The range-based representation of parameter values delivers formal model of AMS system for the considered parameter set. Hence, its simulation results in the range-based system response containing the set of simulation traces reachable for all parameter values lying in the specified ranges. The applicability and efficiency of the proposed simulation-based formal method is shown through the verification of PLL phase properties with respect to frequency.