Master of Science

thesisThis document describes an improved method of formal verification of complex analog/mixed-signal (AMS) circuits. Currently, in our LEMA tool, verification properties are encoded using labeled Petri net (LPN). These LPNs are generated manually, a tedious process that requires the user to have considerable familiarity with the tool. To eliminate this time-consuming process, our LEMA tool is extended to include a translator that converts properties written in a property specification language to LPNs. New methods are also implemented to separate the transient period from the stable output period, thus improving the generated model. Also, the current methodology generates the circuit models for the input values used during the simulation of the circuit. So, models generated for other control input values are not accurate. In this case, accuracy of the generated models is improved by using a linear abstraction method like interpolation

Synchronous Digital Circuits as Functional Programs

Functional programming techniques have been used to describe synchronous digital circuits since the early 1980s and have proven successful at describing certain types of designs. Here we survey the systems and formal underpinnings that constitute this tradition. We situate these techniques with respect to other formal methods for hardware design and discuss the work yet to be done

Towards the automated modelling and formal verification of analog designs

The verification of analog circuits remains a very time consuming and expensive part of the design process. Complete simulation of the state space is not possible; a line is drawn by the designer when it is deemed that enough sets of inputs and outputs have been covered and therefore the circuit is "verified". Unfortunately, bugs could still exist and for safety critical applications this is not acceptable. As well, a bug in the design could lead to costly recalls and a loss of revenue. Formal methods, which use mathematical logic to prove correctness of a design have been developed. However, available techniques for the formal verification of analog circuits are plagued by inaccuracies and a high level of user effort and interaction. We propose in this thesis a complete methodology for the modelling and formal verification of analog circuits. Bond graphs, which are based on the flow of power, are used to automatically extract the circuit's system of Ordinary Differential Equations. Subsequently, two formal verification methods, one based on automated theorem proving with MetiTarski, the other on predicate abstraction based model checking with HybridSal, are then used to verify functional properties on the extracted models. The methodology proposed is mechanical in nature and can be made completely automated. We apply this modelling and verification methodology on a set of analog designs that exhibit complex non-linear behaviour

Doctor of Philosophy

dissertationThe increasing demand for smaller, more efficient circuits has created a need for both digital and analog designs to scale down. Digital technologies have been successful in meeting this challenge, but analog circuits have lagged behind due to smaller transistor sizes having a disproportionate negative affect. Since many applications require small, low-power analog circuits, the trend has been to take advantage of digital's ability to scale by replacing as much of the analog circuitry as possible with digital counterparts. The results are known as \emph{digitally-intensive analog/mixed-signal} (AMS) circuits. Though such circuits have helped the scaling problem, they have further complicated verification. This dissertation improves on techniques for AMS property specifications, as well as, develops sound, efficient extensions to formal AMS verification methods. With the \emph{language for analog/mixed-signal properties} (LAMP), one has a simple intuitive language for specifying AMS properties. LAMP provides a more procedural method for describing properties that is more straightforward than temporal logic-like languages. However, LAMP is still a nascent language and is limited in the types of properties it is capable of describing. This dissertation extends LAMP by adding statements to ignore transient periods and be able to reset the property check when the environment conditions change. After specifying a property, one needs to verify that the circuit satisfies the property. An efficient method for formally verifying AMS circuits is to use the restricted polyhedral class of \emph{zones}. Zones have simple operations for exploring the reachable state space, but they are only applicable to circuit models that utilize constant rates. To extend zones to more general models, this dissertation provides the theory and implementation needed to soundly handle models with ranges of rates. As a second improvement to the state representation, this dissertation describes how octagons can be adapted to model checking AMS circuit models. Though zones have efficient algorithms, it comes at a cost of over-approximating the reachable state space. Octagons have similarly efficient algorithms while adding additional flexibility to reduce the necessary over-approximations. Finally, the full methodology described in this dissertation is demonstrated on two examples. The first example is a switched capacitor integrator that has been studied in the context of transforming the original formal model to use only single rate assignments. Th property of not saturating is written in LAMP, the circuit is learned, and the property is checked against a faulty and correct circuit. In addition, it is shown that the zone extension, and its implementation with octagons, recovers all previous conclusions with the switched capacitor integrator without the need to translate the model. In particular, the method applies generally to all the models produced and does not require the soundness check needed by the translational approach to accept positive verification results. As a second example, the full tool flow is demonstrated on a digital C-element that is driven by a pair of RC networks, creating an AMS circuit. The RC networks are chosen so that the inputs to the C-element are ordered. LAMP is used to codify this behavior and it is verified that the input signals change in the correct order for the provided SPICE simulation traces

Integrating specification and test requirements as constraints in verification strategies for 2D and 3D analog and mixed signal designs

Analog and Mixed Signal (AMS) designs are essential components of today’s modern Integrated Circuits (ICs) used in the interface between real world signals and the digital world. They present, however, significant verification challenges. Out-of-specification failures in these systems have steadily increased, and have reached record highs in recent years. Increasing design complexity, incomplete/wrong specifications (responsible for 47% of all non functional ICs) as well as additional challenges faced when testing these systems are obvious reasons. A particular example is the escalating impact of realistic test conditions with respect to physical (interface between the device under test (DUT) and the test instruments, input-signal conditions, input impedance, etc.), functional (noise, jitter) and environmental (temperature) constraints. Unfortunately, the impact of such constraints could result in a significant loss of performance and design failure even if the design itself was flawless. Current industrial verification methodologies, each addressing specific verification challenges, have been shown to be useful for detecting and eliminating design failures. Nevertheless, decreases in first pass silicon success rates illustrate the lack of cohesive, efficient techniques to allow a predictable verification process that leads to the highest possible confidence in the correctness of AMS designs. In this PhD thesis, we propose a constraint-driven verification methodology for monitoring specifications of AMS designs. The methodology is based on the early insertion of test(s) associated with each design specification. It exploits specific constraints introduced by these planned tests as well as by the specifications themselves, as they are extracted and used during the verification process, thus reducing the risk of costly errors caused by incomplete, ambiguous or missing details in the specification documents. To fully analyze the impact of these constraints on the overall AMS design behavior, we developed a two-phase algorithm that automatically integrates them into the AMS design behavioral model and performs the specifications monitoring in a Matlab simulation environment. The effectiveness of this methodology is demonstrated for two-dimensional (2D) and three-dimensional (3D) ICs. Our results show that our approach can predict out-of-specification failures, corner cases that were not covered using previous verification methodologies. On one hand, we show that specifications satisfied without specification and test-related constraints have failed in the presence of these additional constraints. On the other hand, we show that some specifications may degrade or even cannot be verified without adding specific specification and test-related constraints

Techniques for the formal verification of analog and mixed- signal designs

Embedded systems are becoming a core technology in a growing range of electronic devices. Cornerstones of embedded systems are analog and mixed signal (AMS) designs, which are integrated circuits required at the interfaces with the real world environment. The verification of AMS designs is concerned with the assurance of correct functionality, in addition to checking whether an AMS design is robust with respect to different types of inaccuracies like parameter tolerances, nonlinearities, etc. The verification framework described in this thesis is composed of two proposed methodologies each concerned with a class of AMS designs, i.e., continuous-time AMS designs and discrete-time AMS designs. The common idea behind both methodologies is built on top of Bounded Model Checking (BMC) algorithms. In BMC, we search for a counter-example for a property verified against the design model for bounded number of verification steps. If a concrete counter-example is found, then the verification is complete and reports a failure, otherwise, we need to increment the number of steps until property validation is achieved. In general, the verification is not complete because of limitations in time and memory needed for the verification. To alleviate this problem, we observed that under certain conditions and for some classes of specification properties, the verification can be complete if we complement the BMC with other methods such as abstraction and constraint based verification methods. To test and validate the proposed approaches, we developed a prototype implementation in Mathematica and we targeted analog and mixed signal systems, like oscillator circuits, switched capacitor based designs, Delta-Sigma modulators for our initial tests of this approach

Reasoning about analog-level implementations of digital systems

An approach is described for specifying and reasoning about implementations of digital systems that are described at the analog level of abstraction. It is an extension of existing methods that use higher-order logic for reasoning about implementations described in terms of ideal components at the digital level of abstraction. The behaviour of analog components (transistors, etc) are conservatively specified by predicates on the analog voltages and currents at their terminals. A syntactically defined class of specifications is identified that has been found both to be adequately expressive and also to possess computationally tractable decision procedures. The overall approach is illustrated by deriving the conditions for correctness and for compositionality of TTL implementations of logic gates

Arrows for knowledge-based circuits

Knowledge-based programs (KBPs) are a formalism for directly relating agents' knowledge and behaviour in a way that has proven useful for specifying distributed systems. Here we present a scheme for compiling KBPs to executable automata in finite environments with a proof of correctness in Isabelle/HOL. We use Arrows, a functional programming abstraction, to structure a prototype domain-specific synchronous language embedded in Haskell. By adapting our compilation scheme to use symbolic representations we can apply it to several examples of reasonable size