19 research outputs found

    Reduction of co-simulation runtime through parallel processing

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    During the design phase of modern digital and mixed signal devices, simulations are run to determine the fitness of the proposed design. Some of these simulations can take large amounts of time, thus slowing down the time to manufacture of the system prototype. One of the typical simulations that is done is an integration simulation that simulates the hardware and software at the same time. Most simulators used in this task are monolithic simulators. Some simulators do have the ability to have external libraries and simulators interface with it, but the setup can be a tedious task. This thesis proposes, implements and evaluates a distributed simulator called PDQScS, that allows for speed up of the simulation to reduce this bottleneck in the design cycle without the tedious separation and linking by the user. Using multiple processes and SMP machines a simulation run time reduction was found

    Dynamic Assertion-Based Verification for SystemC

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    SystemC has emerged as a de facto standard modeling language for hardware and embedded systems. However, the current standard does not provide support for temporal specifications. Specifically, SystemC lacks a mechanism for sampling the state of the model at different types of temporal resolutions, for observing the internal state of modules, and for integrating monitors efficiently into the model's execution. This work presents a novel framework for specifying and efficiently monitoring temporal assertions of SystemC models that removes these restrictions. This work introduces new specification language primitives that (1) expose the inner state of the SystemC kernel in a principled way, (2) allow for very fine control over the temporal resolution, and (3) allow sampling at arbitrary locations in the user code. An efficient modular monitoring framework presented here allows the integration of monitors into the execution of the model, while at the same time incurring low overhead and allowing for easy adoption. Instrumentation of the user code is automated using Aspect-Oriented Programming techniques, thereby allowing the integration of user-code-level sample points into the monitoring framework. While most related approaches optimize the size of the monitors, this work focuses on minimizing the runtime overhead of the monitors. Different encoding configurations are identified and evaluated empirically using monitors synthesized from a large benchmark of random and pattern temporal specifications. The framework and approaches described in this dissertation allow the adoption of assertion-based verification for SystemC models written using various levels of abstraction, from system level to register-transfer level. An advantage of this work is that many existing specification languages call be adopted to use the specification primitives described here, and the framework can easily be integrated into existing implementations of SystemC

    Continuous/Discrete Co-Simulation Interfaces from Formalization to Implementation

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    ABSTRACT Today’s systems-on-chip are growing in complexity as a result of a higher density of components on the same chip, and also on account of the heterogeneity of different modules that are particular to different application domains (i.e. mechanical, electrical, optical, biological and chemical). These systems can be found in a broad and diverse spectrum of applications in many industries, including but not limited to Automotive, Aerospace, Health Care and, Consumer Electronics. These multi-domain heterogeneous systems enable new applications and the creation of new markets. This thesis focuses on the design and the simulation of heterogeneous embedded systems, more specifically on continuous/discrete heterogeneous systems. Continuous-time and discrete-event models are at the core of the design of multi-domain systems. We present here a generic, language independent methodology for the design of continuous/discrete heterogeneous systems. This methodology is the basis for design of a new framework providing the interfaces that are in charge with the heterogeneous components adaptation. The methodology was successfully used for the implementation of different continuous/discrete systems such as: a glycemia level regulator, an analog/digital converter, a PID controller, a production chain control system and wimax system. Parts of the proposed methodology were adapted for the formalization, modeling and verification of an optical network on chip.---------- RÉSUMÉ Les systĂšmes sur puce sont de plus en plus complexes, pas seulement en terme de densitĂ© de composants sur la mĂȘme puce mais aussi en terme d‘hĂ©tĂ©rogĂ©nĂ©itĂ© des modules spĂ©cifiques pour diffĂ©rents domaines d’application (mĂ©canique, Ă©lectrique, optique, biologique chimique). On retrouve ces systĂšmes dans un grand Ă©ventail d’applications et dans divers industries tels que l’automobile, l’aĂ©ronautique, la santĂ©, l’électroniques et autres. Ces systĂšmes hĂ©tĂ©rogĂšnes multi-domaine permettent de nouvelles applications et la crĂ©ation de nouveaux marchĂ©s. Cette thĂšse se concentre sur la conception et la simulation des systĂšmes hĂ©tĂ©rogĂšnes embarquĂ©s. Les modĂšles temps-continu et Ă©vĂ©nement discret sont le noyau de la conception des systĂšmes multi-domaine. On prĂ©sente ici l’analyse de modĂšles d’exĂ©cution et modĂšles de synchronisation des systĂšmes hĂ©tĂ©rogĂšnes continu/discret, la dĂ©finition d’une mĂ©thodologie gĂ©nĂ©rique pour la conception des outils de co-simulation des systĂšmes hĂ©tĂ©rogĂšnes continus/discrets et la validation de la mĂ©thodologie par applications – la rĂ©alisation d’un cadre de co-simulation pour les systĂšmes continu/discret. La mĂ©thodologie exploite les techniques de vĂ©rification formelle et de la simulation. La conception des outils de simulation est basĂ©e sur la dĂ©finition d’une architecture gĂ©nĂ©rique des interfaces de simulation ainsi que sur des modĂšles de synchronisation vĂ©rifiĂ©s formellement. La mĂ©thodologie a Ă©tĂ© utilisĂ©e pour l’implĂ©mentation d’un rĂ©gulateur de niveau de glycĂ©mie. Une partie de la mĂ©thodologie a Ă©tĂ© adaptĂ©e pour la formalisation, la modĂ©lisation et la vĂ©rification formelle d’un rĂ©seau optique sur puce

    Timing verification in transaction modeling

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    Les systĂšmes MatĂ©riels/Logiciels deviennent indispensables dans tous les aspects de la vie quotidienne. La prĂ©sence croissante de ces systĂšmes dans les diffĂ©rents produits et services incite Ă  trouver des mĂ©thodes pour les dĂ©velopper efficacement. Mais une conception efficace de ces systĂšmes est limitĂ©e par plusieurs facteurs, certains d'entre eux sont: la complexitĂ© croissante des applications, une augmentation de la densitĂ© d'intĂ©gration, la nature hĂ©tĂ©rogĂšne des produits et services, la diminution de temps d’accĂšs au marchĂ©. Une modĂ©lisation transactionnelle (TLM) est considĂ©rĂ©e comme un paradigme prometteur permettant de gĂ©rer la complexitĂ© de conception et fournissant des moyens d’exploration et de validation d'alternatives de conception Ă  des niveaux d’abstraction Ă©levĂ©s. Cette recherche propose une mĂ©thodologie d’expression de temps dans TLM basĂ©e sur une analyse de contraintes temporelles. Nous proposons d'utiliser une combinaison de deux paradigmes de dĂ©veloppement pour accĂ©lĂ©rer la conception: le TLM d'une part et une mĂ©thodologie d’expression de temps entre diffĂ©rentes transactions d’autre part. Cette synergie nous permet de combiner dans un seul environnement des mĂ©thodes de simulation performantes et des mĂ©thodes analytiques formelles. Nous avons proposĂ© un nouvel algorithme de vĂ©rification temporelle basĂ© sur la procĂ©dure de linĂ©arisation des contraintes de type min/max et une technique d'optimisation afin d'amĂ©liorer l'efficacitĂ© de l'algorithme. Nous avons complĂ©tĂ© la description mathĂ©matique de tous les types de contraintes prĂ©sentĂ©es dans la littĂ©rature. Nous avons dĂ©veloppĂ© des mĂ©thodes d'exploration et raffinement de systĂšme de communication qui nous a permis d'utiliser les algorithmes de vĂ©rification temporelle Ă  diffĂ©rents niveaux TLM. Comme il existe plusieurs dĂ©finitions du TLM, dans le cadre de notre recherche, nous avons dĂ©fini une mĂ©thodologie de spĂ©cification et simulation pour des systĂšmes MatĂ©riel/Logiciel basĂ©e sur le paradigme de TLM. Dans cette mĂ©thodologie plusieurs concepts de modĂ©lisation peuvent ĂȘtre considĂ©rĂ©s sĂ©parĂ©ment. BasĂ©e sur l'utilisation des technologies modernes de gĂ©nie logiciel telles que XML, XSLT, XSD, la programmation orientĂ©e objet et plusieurs autres fournies par l’environnement .Net, la mĂ©thodologie proposĂ©e prĂ©sente une approche qui rend possible une rĂ©utilisation des modĂšles intermĂ©diaires afin de faire face Ă  la contrainte de temps d’accĂšs au marchĂ©. Elle fournit une approche gĂ©nĂ©rale dans la modĂ©lisation du systĂšme qui sĂ©pare les diffĂ©rents aspects de conception tels que des modĂšles de calculs utilisĂ©s pour dĂ©crire le systĂšme Ă  des niveaux d’abstraction multiples. En consĂ©quence, dans le modĂšle du systĂšme nous pouvons clairement identifier la fonctionnalitĂ© du systĂšme sans les dĂ©tails reliĂ©s aux plateformes de dĂ©veloppement et ceci mĂšnera Ă  amĂ©liorer la "portabilitĂ©" du modĂšle d'application.Hardware/Software (Hw/Sw) systems are likely to become essential in all aspects of everyday life. The increasing penetration of Hw/Sw systems in products and services creates a necessity of their efficient development. However, the productive design of these systems is limited by several factors, some of them being the increasing complexity of applications, the increasing degree of integration, the heterogeneous nature of products and services as well as the shrinking of the time-to-market delay. Transaction Level Modeling (TLM) paradigm is considered as one of the most promising simulation paradigms to break down the design complexity by allowing the exploration and validation of design alternatives at high levels of abstraction. This research proposes a timing expression methodology in TLM based on temporal constraints analysis. We propose to use a combination of two paradigms to accelerate the design process: TLM on one hand and a methodology to express timing between different transactions on the other hand. Using a timing specification model and underlining timing constraints verification algorithms can decrease the time needed for verification by simulation. Combining in one framework the simulation and analytical design exploration methods can improve the analytical power of design verification and validation. We have proposed a new timing verification algorithm based on the linearization procedure and an optimization technique to improve its efficiency. We have completed the mathematical representation of all constraint types discussed in the literature creating in this way a unified timing specification methodology that can be used in the expression of a wider class of applications than previously presented ones. We have developed the methods for communication structure exploration and refinement that permitted us to apply the timing verification algorithms in system exploration at different TLM levels. As there are many definitions of TLM and many development environments proposing TLM in their design cycle with several pro and contra, in the context of our research we define a hardware/software (Hw/Sw) specification and simulation methodology which supports TLM in such a way that several modeling concepts can be seen separately. Relying on the use of modern software engineering technologies such as XML, XSLT, XSD, object oriented programming and others supported by the .Net Framework, an approach that makes an intermediate design model reuse possible in order to cope with time-to-market constraint is presented. The proposed TLM design methodology provides a general approach in system modeling that separates various application modeling aspects from system specification: computational models, used in application modeling, supported by the language used for the functional specification and provided by simulator. As a result, in the system model we can clearly identify system functionality without details related to the development platform thereby leading to a better “portability” of the application model

    Timing model derivation : pipeline analyzer generation from hardware description languages

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    Safety-critical systems are forced to finish their execution within strict deadlines so that worst-case execution time (WCET) guarantees are a crucial part of their verification. Timing models of the analyzed hardware form the basis for static analysis-based approaches like the aiT WCET analyzer. Currently, timing models are hand-crafted based on frequently incorrect documentation causing the process to be error-prone and time-consuming. This thesis bridges the gap between automatic hardware synthesis and WCET analysis development by introducing a process for the derivation of timing models from VHDL specifications. We propose a set of transformations and abstractions to reduce the hardware design\u27s complexity enabling the generation of efficient and provably correct WCET analyzers. They employ an abstract interpretation-based simulation of program executions based on a defined abstract simulation semantics. We have defined workflow patterns showing how to gradually apply the derivation process to VHDL models, thereby removing timing-irrelevant constructs. Interval property checking is used to validate the transformations. A further contribution of this thesis is the implementation of a tool set that realizes the introduced derivation process and shows its applicability to non-trivial industrial designs in experimental evaluations. Influences on design choices to the quality of the derived timing model are presented building an informal predictability notion for VHDL.Sicherheits-kritische Systeme unterliegen oft der Einhaltung strikter Laufzeitschranken, weshalb zur Verifikation sichere Obergrenzen der Laufzeit im schlimmsten Fall (WCET) bestimmt werden. Zeitmodelle der analysierten Hardware sind hierbei die Grundlage fĂŒr auf statischen Analysen basierende Verfahren. Aktuell werden solche Modelle hĂ€ndisch aus HandbĂŒchern extrahiert, ein sehr zeitaufwĂ€ndiger und fehleranfĂ€lliger Prozess. Diese Arbeit schlĂ€gt eine BrĂŒcke zwischen automatischer Hardware-Synthese und der Entwicklung von WCET-Analysen durch die EinfĂŒhrung eines Ableitungsprozesses von Zeitmodellen aus VHDL-Spezifikationen. Transformationen und Abstraktionen werden zur KomplexitĂ€tsreduktion eingesetzt, um die Erzeugung von effizienten und beweisbar korrekten Analysatoren zu ermöglichen. Selbige bedienen sich abstrakter Interpretation von ProgrammausfĂŒhrungen basierend auf einer Simulations-Semantik. Definierte ArbeitsablĂ€ufe zeigen, wie man die Ableitung schrittweise auf VHDL-Modellen umsetzt und dadurch fĂŒr das Zeitverhalten irrelevante Teile des Modells entfernt. Interval Property Checking gewĂ€hrleistet hierbei, dass die Transformationen semantik-erhaltend sind. Eine Tool-Implementierung realisiert den vorgestellen Ableitungsprozess und unterstreicht seine Anwendbarkeit auf komplexe industrielle Designs durch experimentelle untersuchungen. Außerdem werden VHDL-Designentscheidungen hinsicht ihres Einflusses auf die QualitĂ€t des abgeleiteten Zeitmodells betrachtet

    Complete Model-Based Testing Applied to the Railway Domain

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    Testing is the most important verification technique to assert the correctness of an embedded system. Model-based testing (MBT) is a popular approach that generates test cases from models automatically. For the verification of safety-critical systems, complete MBT strategies are most promising. Complete testing strategies can guarantee that all errors of a certain kind are revealed by the generated test suite, given that the system-under-test fulfils several hypotheses. This work presents a complete testing strategy which is based on equivalence class abstraction. Using this approach, reactive systems, with a potentially infinite input domain but finitely many internal states, can be abstracted to finite-state machines. This allows for the generation of finite test suites providing completeness. However, for a system-under-test, it is hard to prove the validity of the hypotheses which justify the completeness of the applied testing strategy. Therefore, we experimentally evaluate the fault-detection capabilities of our equivalence class testing strategy in this work. We use a novel mutation-analysis strategy which introduces artificial errors to a SystemC model to mimic typical HW/SW integration errors. We provide experimental results that show the adequacy of our approach considering case studies from the railway domain (i.e., a speed-monitoring function and an interlocking-system controller) and from the automotive domain (i.e., an airbag controller). Furthermore, we present extensions to the equivalence class testing strategy. We show that a combination with randomisation and boundary-value selection is able to significantly increase the probability to detect HW/SW integration errors

    A unified model for hardware/software codesign

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    Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2011.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Cataloged from student submitted PDF version of thesis.Includes bibliographical references (p. 179-188).Embedded systems are almost always built with parts implemented in both hardware and software. Market forces encourage such systems to be developed with dierent hardware-software decompositions to meet dierent points on the price-performance-power curve. Current design methodologies make the exploration of dierent hardware-software decompositions difficult because such exploration is both expensive and introduces signicant delays in time-to-market. This thesis addresses this problem by introducing, Bluespec Codesign Language (BCL), a united language model based on guarded atomic actions for hardware-software codesign. The model provides an easy way of specifying which parts of the design should be implemented in hardware and which in software without obscuring important design decisions. In addition to describing BCL's operational semantics, we formalize the equivalence of BCL programs and use this to mechanically verify design refinements. We describe the partitioning of a BCL program via computational domains and the compilation of dierent computational domains into hardware and software, respectively.by Nirav Dave.Ph.D

    Parallele und kooperative Simulation fĂŒr eingebettete Multiprozessorsysteme

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    Die Entwicklung von eingebetteten Systemen wird durch die stetig steigende Anzahl und Integrationsdichte neuer Funktionen in Kombination mit einem erhöhten Interaktionsgrad zunehmend zur Herausforderung. Vor diesem Hintergrund werden in dieser Arbeit Methoden zur SystemC-basierten parallelen Simulation von Multiprozessorsystemen auf Manycore Architekturen sowie zur Verbesserung der InteroperabilitÀt zwischen heterogenen Simulationswerkzeugen entwickelt, experimentell untersucht und bewertet

    Tenth Workshop and Tutorial on Practical Use of Coloured Petri Nets and the CPN Tools Aarhus, Denmark, October 19-21, 2009

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    This booklet contains the proceedings of the Tenth Workshop on Practical Use of Coloured Petri Nets and the CPN Tools, October 19-21, 2009. The workshop is organised by the CPN group at the Department of Computer Science, University of Aarhus, Denmark. The papers are also available in electronic form via the web pages: http://www.cs.au.dk/CPnets/events/workshop0

    Formale Verifikationsmethodiken fĂŒr nichtlineare analoge Schaltungen

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    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 AnsĂ€tze in den Bereichen verifikationsgerechte diskrete Modellierung analoger Schaltungen, Spezifikation analoger Schaltungseigenschaften und formale Verifikationsalgorithmen vorgestellt. Ausgehend vom Stand der Technik der Modellierung analoger Schaltungen fĂŒr die simulationsbasierte Verifikation wird im Rahmen dieser Arbeit die diskrete Modellierung analoger Schaltungen fĂŒr 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 ZustĂ€nden fĂŒr 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 AnsĂ€tzen 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 AnsĂ€tze fĂŒr 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 natĂŒrlichsprachlichen Kapselung temporallogischer Operationen, die mit erweiterten Algorithmen zur Transitionspfadbestimmung, DurchfĂŒhrung von Berechnungen auf Zustandsparametern und Oszillationsbestimmung eine hohe AusdrucksstĂ€rke 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 fĂŒr Eigenschaften eines vollstĂ€ndigen diskreten Modells ohne Modifikation auch auf Simulationsergebnissen ausgewertet werden. Ein fĂŒr das formale ASL-basierte Model Checking entwickelter Ansatz zur Erzeugung von Gegenbeispielen fĂŒr 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 vollstĂ€ndig den Zustandsraum einer Schaltung abdeckenden Eingangsstimuli entwickelt. Die vollstĂ€ndig 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 vollstĂ€ndig den Zustandsraum abdeckenden Eingangsstimuli ersetzt die anwenderdefinierten Eingangsstimuli durch die vollstĂ€ndig den Zustandsraum abdeckenden. So kann die Äquivalenz fĂŒr jeden möglichen Zustand der zu vergleichenden Implementierungen anhand eines automatisierten Vergleichs der Simulationsergebnisse beider Implementierungen gezeigt werden. Um die Ergebnisse der neu eingefĂŒhrten formalen Verifikationsmethodiken visuell zu untersuchen wurde ein Verfahren entwickelt, das den Zustandsraum und seine Dynamik mittels eines Partikel-Simulationsansatzes visualisiert. Da die Partikel ĂŒber den gesamten Zustandsraum randomisiert verteilt werden und sich dann gemĂ€ĂŸ der Vektorfelddynamik fortbewegen, kann auch hier ein Einblick in das Systemverhalten gewonnen werden, der eine weitestgehend vollstĂ€ndige und somit formale ReprĂ€sentation des Zustandsraums bietet. Die prototypische Implementierung der im Rahmen dieser Arbeit entwickelten formalen Verifikationsmethodiken wurde auf zahlreiche Beispielschaltungen angewendet. Die Ergebnisse fĂŒr die neuen AnsĂ€tze zur diskreten Modellierung, zur Spezifikation und zu Verifikationsalgorithmen analoger Schaltungen zeigen, dass die aus diesen AnsĂ€tzen erzeugten Verifikationsmethodiken erfolgreich auf komplexe Zustandsraumstrukturen angewendet werden können
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