Formal hardware verification of digital circuits

The use of formal methods to verify the correctness of digital circuits is less constrained by the growing complexity of digital circuits than conventional methods based on exhaustive simulation. This paper briefly outlines three main approaches to formal hardware verification: symbolic simulation, state machine analysis, and theorem-proving

LEMA: A tool for the formal verification of digitally-intensive analog/mixed-signal circuits

pre-printThe increasing integration of analog/mixed-signal (AMS) circuits into system designs has further complicated an already difficult verification problem. Recently, formal verification, which has been successful in the purely digital domain, has made some in-roads in the AMS domain. This paper describes one such formal verification tool for AMS circuits, LEMA. In particular, LEMA is capable of generating a formal model from simulation traces that, when coupled with a formal property provided in our new property language, can be model checked with one of three model checkers within LEMA. This paper briefly describes the capabilities of the LEMA AMS verification tool flow

New developments in the theory of Groebner bases and applications to formal verification

We present foundational work on standard bases over rings and on Boolean Groebner bases in the framework of Boolean functions. The research was motivated by our collaboration with electrical engineers and computer scientists on problems arising from formal verification of digital circuits. In fact, algebraic modelling of formal verification problems is developed on the word-level as well as on the bit-level. The word-level model leads to Groebner basis in the polynomial ring over Z/2n while the bit-level model leads to Boolean Groebner bases. In addition to the theoretical foundations of both approaches, the algorithms have been implemented. Using these implementations we show that special data structures and the exploitation of symmetries make Groebner bases competitive to state-of-the-art tools from formal verification but having the advantage of being systematic and more flexible.Comment: 44 pages, 8 figures, submitted to the Special Issue of the Journal of Pure and Applied Algebr

VeriSFQ - A Semi-formal Verification Framework and Benchmark for Single Flux Quantum Technology

In this paper, we propose a semi-formal verification framework for single-flux quantum (SFQ) circuits called VeriSFQ, using the Universal Verification Methodology (UVM) standard. The considered SFQ technology is superconducting digital electronic devices that operate at cryogenic temperatures with active circuit elements called the Josephson junction, which operate at high switching speeds and low switching energy - allowing SFQ circuits to operate at frequencies over 300 gigahertz. Due to key differences between SFQ and CMOS logic, verification techniques for the former are not as advanced as the latter. Thus, it is crucial to develop efficient verification techniques as the complexity of SFQ circuits scales. The VeriSFQ framework focuses on verifying the key circuit and gate-level properties of SFQ logic: fanout, gate-level pipeline, path balancing, and input-to-output latency. The combinational circuits considered in analyzing the performance of VeriSFQ are: Kogge-Stone adders (KSA), array multipliers, integer dividers, and select ISCAS'85 combinational benchmark circuits. Methods of introducing bugs into SFQ circuit designs for verification detection were experimented with - including stuck-at faults, fanout errors, unbalanced paths, and functional bugs like incorrect logic gates. In addition, we propose an SFQ verification benchmark consisting of combinational SFQ circuits that exemplify SFQ logic properties and present the performance of the VeriSFQ framework on these benchmark circuits. The portability and reusability of the UVM standard allows the VeriSFQ framework to serve as a foundation for future SFQ semi-formal verification techniques.Comment: 7 pages, 6 figures, 4 tables; submitted, accepted, and presented at ISQED 2019 (20th International Symposium on Quality Electronic Design) on March 7th, 2019 in Santa Clara, CA, US

An optimized method towards formal verification of mixed signals using differential fed neural network over FFNN

Today, the semiconductor industries are rapidly usinganalog and mixed signals to achieve cost-effective solutions on a System on Chip (SoC) design.  The SoC device is a part of analog, digital and essential mixed-signal models/circuits merged on a semiconductor device, which provides the platform to build modern retail/consumer electronics appliances with smart technology. In order to evaluate the mixed signals, the conventional approaches are not effective with respect to its performance, time and manufacturing cost. Thus, the recent researches were much interested in formal verification technique as it provides the evidence of conscious algorithms in a system. The demand for formal verification in the SoC designs in the context of software and hardware platform is high because of its cost and accuracy. Thus, the paper introduces atechnique of formal verification for mixed signals by using training models of the Differential fed neural network (DFNN) over feedforward neural network (FFNN). The formal verification is performed through equivalence checking by using recently adopted designs as reference designs. The outcomes of the verification techniques suggests that DFNN based technique improves the training accuracy and optimizes the hardware resources like area, power than the FFNN based technique

Compositional circuit design with asynchronous concepts

PhD ThesisSynchronous circuits are pervasive in modern digital systems, such as smart-phones, wearable devices and computers. Synchronous circuits are controlled by a global clock signal, which greatly simplifies their design but is also a limitation in some applications. Asynchronous circuits are a logical alternative: they do not use a global clock to synchronise their components. Instead, every component reacts to input events at the rate they occur. Asynchronous circuits are not widely adopted by industry, because they are often harder to design and require more sophisticated tools and formal models. Signal Transition Graphs (STGs) is a well-studied formal model for the specification, verification and synthesis of asynchronous circuits with state-of-the-art tool support. STGs use a graphical notation where vertices and arcs specify the operation of an asynchronous circuit. These graphical specifications can be difficult to describe compositionally, and provide little reusability of useful sections of a graph. In this thesis we present Asynchronous Concepts, a new design methodology for asynchronous circuit design. A concept is a self-contained description of a circuit requirement, which is composable with any other concept, allowing compositional specification of large asynchronous circuits. Concepts can be shared, reused and extended by users, promoting the reuse of behaviours within single or multiple specifications. Asynchronous Concepts can be translated to STGs to benefit from the existing theory and tools developed by the asynchronous circuits community. Plato is a software tool developed for Asynchronous Concepts that supports the presented design methodology, and provides automated methods for translation to STGs. The design flow which utilises Asynchronous Concepts is automated using Plato and the open-source toolsuite Workcraft, which can use the translated STGs in verification and synthesis using integrated tools. The proposed language, the design flow, and the supporting tools are evaluated on real-world case studies

Analog and Mixed Signal Verification

More and more electronic systems have components that are not purely digital. Verification of such systems is a much less developed discipline than the digital equivalents and the application of formal (mathematically complete) techniques is a nascent area. In this paper, we will discuss the nature of analog circuit design and describe the way verification is done in practice today. We will describe some “formal” approaches coming from the analog design community. We will describe some of the approaches to formal verification that have been presented in recent literature. Finally, we will mention some areas where there are opportunities for future work

Formale Verifikationsmethodiken für nichtlineare analoge Schaltungen

The objective of this thesis is to develop new methodologies for formal verification of nonlinear analog circuits. Therefore, new approaches to discrete modeling of analog circuits, specification of analog circuit properties and formal verification algorithms are introduced. Formal approaches to verification of analog circuits are not yet introduced into industrial design flows and still subject to research. Formal verification proves specification conformance for all possible input conditions and all possible internal states of a circuit. Automatically proving that a model of the circuit satisfies a declarative machine-readable property specification is referred to as model checking. Equivalence checking proves the equivalence of two circuit implementations. Starting from the state of the art in modeling analog circuits for simulation-based verification, discrete modeling of analog circuits for state space-based formal verification methodologies is motivated in this thesis. In order to improve the discrete modeling of analog circuits, a new trajectory-directed partitioning algorithm was developed in the scope of this thesis. This new approach determines the partitioning of the state space parallel or orthogonal to the trajectories of the state space dynamics. Therewith, a high accuracy of the successor relation is achieved in combination with a lower number of states necessary for a discrete model of equal accuracy compared to the state-of-the-art hyperbox-approach. The mapping of the partitioning to a discrete analog transition structure (DATS) enables the application of formal verification algorithms. By analyzing digital specification concepts and the existing approaches to analog property specification, the requirements for a new specification language for analog properties have been discussed in this thesis. On the one hand, it shall meet the requirements for formal specification of verification approaches applied to DATS models. On the other hand, the language syntax shall be oriented on natural language phrases. By synthesis of these requirements, the analog specification language (ASL) was developed in the scope of this thesis. The verification algorithms for model checking, that were developed in combination with ASL for application to DATS models generated with the new trajectory-directed approach, offer a significant enhancement compared to the state of the art. In order to prepare a transition of signal-based to state space-based verification methodologies, an approach to transfer transient simulation results from non-formal test bench simulation flows into a partial state space representation in form of a DATS has been developed in the scope of this thesis. As has been demonstrated by examples, the same ASL specification that was developed for formal model checking on complete discrete models could be evaluated without modifications on transient simulation waveforms. An approach to counterexample generation for the formal ASL model checking methodology offers to generate transition sequences from a defined starting state to a specification-violating state for inspection in transient simulation environments. Based on this counterexample generation, a new formal verification methodology using complete state space-covering input stimuli was developed. By conducting a transient simulation with these complete state space-covering input stimuli, the circuit adopts every state and transition that were visited during stimulus generation. An alternative formal verification methodology is given by retransferring the transient simulation responses to a DATS model and by applying the ASL verification algorithms in combination with an ASL property specification. Moreover, the complete state space-covering input stimuli can be applied to develop a formal equivalence checking methodology. Therewith, the equivalence of two implementations can be proven for every inner state of both systems by comparing the transient simulation responses to the complete-coverage stimuli of both circuits. In order to visually inspect the results of the newly introduced verification methodologies, an approach to dynamic state space visualization using multi-parallel particle simulation was developed. Due to the particles being randomly distributed over the complete state space and moving corresponding to the state space dynamics, another perspective to the system's behavior is provided that covers the state space and hence offers formal results. The prototypic implementations of the formal verification methodologies developed in the scope of this thesis have been applied to several example circuits. The acquired results for the new approaches to discrete modeling, specification and verification algorithms all demonstrate the capability of the new verification methodologies to be applied to complex circuit blocks and their properties.Gegenstand dieser Dissertation ist die Entwicklung neuer Methodiken zur formalen Verifikation nichtlinearer analoger elektronischer Schaltungen. Dazu werden im Rahmen dieser Arbeit entstandene neue Ansätze in den Bereichen verifikationsgerechte diskrete Modellierung analoger Schaltungen, Spezifikation analoger Schaltungseigenschaften und formale Verifikationsalgorithmen vorgestellt. Ausgehend vom Stand der Technik der Modellierung analoger Schaltungen für die simulationsbasierte Verifikation wird im Rahmen dieser Arbeit die diskrete Modellierung analoger Schaltungen für zustandsraumbasierte formale Verifikationsverfahren betrachtet. Dazu wurde ein neuer Ansatz zur diskreten Modellierung entwickelt, der die Aufteilungsstruktur anhand der Trajektorien der Vektorfelddynamik bestimmt. So wird eine hohe Genauigkeit der Nachfolgerrelation ermöglicht, woraus eine niedrigere Zahl an Zuständen für ein diskretes Modell gleicher Genauigkeit im Vergleich mit dem bisherigen Stand der Technik folgt. Die Abbildung der Trajektorien-gesteuerten Partitionierung auf eine diskrete analoge Transitionsstruktur (DATS) erlaubt die Anwendung von formalen Verifikationsalgorithmen. Die formale Spezifikation von Eigenschaften in ersten Ansätzen zum Model Checking analoger Schaltungen hat sich stark an den bestehenden temporallogischen Verfahren aus dem Bereich digitaler Hardware orientiert. Ausgehend von einer Analyse digitaler Spezifikationskonzepte und der bestehenden Ansätze für analoge Eigenschaften wurden Anforderungen an eine neue Spezifikationssprache in dieser Arbeit abgeleitet. Die aus diesen Anforderungen im Rahmen dieser Arbeit entwickelte analoge Spezifikationssprache "Analog Specification Language" (ASL) basiert auf einer natürlichsprachlichen Kapselung temporallogischer Operationen, die mit erweiterten Algorithmen zur Transitionspfadbestimmung, Durchführung von Berechnungen auf Zustandsparametern und Oszillationsbestimmung eine hohe Ausdrucksstärke analoger Eigenschaften mit einer anwenderfreundlichen Syntax kombinieren konnte. Die zusammen mit ASL entwickelten Model Checking-Verifikationsalgorithmen zur Auswertung von ASL-Spezifikationen auf einem mit dem Trajektorien-gesteuerten Diskretisierungsverfahren erzeugten DATS-Modell bilden eine wesentliche Erweiterung zum Stand der Technik. Um einen Übergang der Verifikation von signalbasierten zu zustandsraumbasierten Methodiken zu ermöglichen, wurde im Rahmen dieser Arbeit ein Ansatz entwickelt, der die Übertragung von transienten Simulationsergebnissen aus nicht-formalen Testbench-Simulationsumgebungen in eine partielle DATS-Zustandsraumdarstellung ermöglicht. Damit kann, wie anhand von Beispielen gezeigt werden konnte, die gleiche ASL-Spezifikation für Eigenschaften eines vollständigen diskreten Modells ohne Modifikation auch auf Simulationsergebnissen ausgewertet werden. Ein für das formale ASL-basierte Model Checking entwickelter Ansatz zur Erzeugung von Gegenbeispielen für als spezifikationsverletzend identifizierte Zustandsraumgebiete erlaubt es, Transitionsfolgen von einem definierten Startzustand zu einem spezifikationsverletzenden Zustand zu ermitteln. Auf Basis dieses Gegenbeispiel-Verfahrens wurde eine neue formale Eigenschaftsverifikationsmethodik mittels vollständig den Zustandsraum einer Schaltung abdeckenden Eingangsstimuli entwickelt. Die vollständig den Zustandsraum abdeckenden Eingangsstimuli bieten noch eine weitere Anwendungsmöglichkeit im Bereich des Äquivalenzvergleichs. Die im Rahmen dieser Arbeit entwickelte Methodik zum formalen Äquivalenzvergleich auf Basis der vollständig den Zustandsraum abdeckenden Eingangsstimuli ersetzt die anwenderdefinierten Eingangsstimuli durch die vollständig den Zustandsraum abdeckenden. So kann die Äquivalenz für jeden möglichen Zustand der zu vergleichenden Implementierungen anhand eines automatisierten Vergleichs der Simulationsergebnisse beider Implementierungen gezeigt werden. Um die Ergebnisse der neu eingeführten formalen Verifikationsmethodiken visuell zu untersuchen wurde ein Verfahren entwickelt, das den Zustandsraum und seine Dynamik mittels eines Partikel-Simulationsansatzes visualisiert. Da die Partikel über den gesamten Zustandsraum randomisiert verteilt werden und sich dann gemäß der Vektorfelddynamik fortbewegen, kann auch hier ein Einblick in das Systemverhalten gewonnen werden, der eine weitestgehend vollständige und somit formale Repräsentation des Zustandsraums bietet. Die prototypische Implementierung der im Rahmen dieser Arbeit entwickelten formalen Verifikationsmethodiken wurde auf zahlreiche Beispielschaltungen angewendet. Die Ergebnisse für die neuen Ansätze zur diskreten Modellierung, zur Spezifikation und zu Verifikationsalgorithmen analoger Schaltungen zeigen, dass die aus diesen Ansätzen erzeugten Verifikationsmethodiken erfolgreich auf komplexe Zustandsraumstrukturen angewendet werden können