Verification is an important step for Integrated Circuit (IC) design. In fact, literature has reported that up to 70% of the design effort is spent on checking if the design is functionally correct. One of the core verification tasks is Equivalence Checking (EC), which attempts to check if two structurally different designs are functionally equivalent for all reachable states. Powerful equivalence checking can also provide opportunities for more aggressive logic optimizations, meeting different goals such as smaller area, better performance, etc. The success of Combinational Equivalence Checking (CEC) has laid a foundation to industry-level combinational logic synthesis and optimization. However, Sequential Equivalence Checking (SEC) still faces much challenge, especially for those complex circuits that have different state encodings and few internal signal equivalences. In this thesis, we propose a novel simulation-based multi-node inductive invariant generation and pruning technique to check the equivalence of sequential circuits that have different state encodings and very few equivalent signals between them. By first grouping flip-flops into smaller subsets to make it scalable for large designs, we then propose a constrained logic synthesis technique to prune potential multi-node invariants without inadvertently losing important constraints. Our pruning technique guarantees the same conclusion for different instances (proving SEC or not) compared to previous approaches in which merging of such potential invariants might lose important relations if the merged relation does not turn out to be a true invariant. Experimental results show that the smaller invariant set can be very effective for sequential equivalence checking of such hard SEC instances. Our approach is up to 20x-- faster compared to previous mining-based methods for larger circuits. / Master of Science

Verification, as opposed to Testing and Post-Silicon Validation, is a critical step for Integrated Circuits (IC) Design, answering the question "Are we designing the right function?" before the chips are manufactured. One of the core areas of Verification is Equivalence Checking (EC), which is a special yet independent case of Model Checking (MC). Equivalence Checking aims to prove that two circuits, when fed with the same inputs, produce the exact same outputs. There are broadly two ways to conduct Equivalence Checking, simulation and Formal Equivalence Checking. Simulation requires one to try out different input combinations and observe if the two circuits produce the same output. Obviously, since it is not possible to enumerate all combinations of different inputs, completeness cannot be guaranteed. On the other hand, Formal Equivalence Checking can achieve 100% confidence. As the number of gates and in particular, the number of flip-flops, in circuits has grown tremendously during the recent years, the problem of Formal Equivalence Checking has become much harder â A recent evaluation of a general-case Formal Equivalence Checking engine [1] shows that about 15% of industrial designs cannot be verified after a typical sequential synthesis flow. As a result, a lot of attention on Formal Equivalence Checking has been drawn both academically and industrially. For years Combinational Equivalence Checking(CEC) has been the pervasive framework for Formal Equivalence Checking(FEC) in the industry. However, due to the limitation of being able to verify circuits only with 1:1 flip-flop pairing, a pure CEC-based methodology requires a full regression of the verification process, meaning that performing sequential optimizations like retiming or FSM re-encoding becomes somewhat of a bottleneck in the design cycle [2]. Therefore, a more powerful framework — Sequential Equivalence Checking (SEC) — has been gradually adopted in industry. In this thesis, we target on Sequential Equivalence Checking by finding efficient yet powerful group of relationships (invariants) among the signals of the two circuits being compared. In order to achieve a high success rate on some of the extremely hard-to-verify circuits, we are interested in both two-node and multi-node (up to 4 nodes) invariants. Also we are interested in invariants among both flip-flops and internal signals. For large circuits, there can be too many potential invariants requiring much time to prove. However, we observed that a large portion of them may not even contribute to equivalence checking. Moreover, equivalence checking can be significantly helped if there exists a method to check if a subset of potential invariants would be sufficient (e.g., whether two-nodes are enough or multi-nodes are also needed) prior to the verification step. Therefore, we propose two sufficiency-based approaches to identify useful invariants out of the initial potential invariants for SEC. Experimental results show that our approach can either demonstrate insufficiency of the invariants or select a small portion of them to successfully prove the equivalence property. Our approaches are quite case-independent and flexible. They can be applied on circuits with different synthesis techniques and combined with other techniques. / Master of Science

With the advances in VLSI and System-On-Chip (SOC) technology, the complexity of hardware systems has increased manifold. Today, 70% of the design cost is spent in verifying these intricate systems. The two most widely used formal methods for design verification are Equivalence Checking and Model Checking. Equivalence Checking requires that the implementation circuit should be exactly equivalent to the specification circuit (golden model). In other words, for each possible input pattern, the implementation circuit should yield the same outputs as the specification circuit. Model checking, on the other hand, checks to see if the design holds certain properties, which in turn are indispensable for the proper functionality of the design. Complexities in both Equivalence Checking and Model Checking are exponential to the circuit size. In this thesis, we firstly propose a novel technique to improve SAT-based Combinational Equivalence Checking (CEC) and Bounded Model Checking (BMC). The idea is to perform a low-cost preprocessing that will statically induce global signal relationships into the original CNF formula of the circuit under verification and hence reduce the complexity of the SAT instance. This efficient and effective preprocessing quickly builds up the implication graph for the circuit under verification, yielding a large set of logic implications composed of direct, indirect and extended backward implications. These two-node implications (spanning time-frame boundaries) are converted into two-literal clauses, and added to the original CNF database. The added clauses constrain the search space of the SAT-solver engine, and provide correlation among the different variables, which enhances the Boolean Constraint Propagation (BCP). Experimental results on large and difficult ISCAS'85, ISCAS'89 (full scan) and ITC'99 (full scan) CEC instances and ISCAS'89 BMC instances show that our approach is independent of the state-of-the-art SAT-solver used, and that the added clauses help to achieve more than an order of magnitude speedup over the conventional approach. Also, comparison with Hyper-Resolution [Bacchus 03] suggests that our technique is much more powerful, yielding non-trivial clauses that significantly simplify the SAT instance complexity. Secondly, we propose a novel global learning technique that helps to identify highly non-trivial relationships among signals in the circuit netlist, thereby boosting the power of the existing implication engine. We call this new class of implications as 'extended forward implications', and show its effectiveness through additional untestable faults they help to identify. Thirdly, we propose a suite of lemmas and theorems to formalize global learning. We show through implementation that these theorems help to significantly simplify a generic CNF formula (from Formal Verification, Artificial Intelligence etc.) by identifying the necessary assignments, equivalent signals, complementary signals and other non-trivial implication relationships among its variables. We further illustrate through experimental results that the CNF formula simplification obtained using our tool outshines the simplification obtained using other preprocessors. / Master of Science

Powerful sequential optimization techniques can drastically change the Integrated Circuit (IC) design paradigm. Due to the limited capability of sequential verification tools, aggressive sequential optimization is shunned nowadays as there is no efficient way to prove the preservation of equivalence after optimization. Due to the fact that the number of transistors fitting on single fixed-size die increases with Moore's law, the problem gets harder over time and in an exponential rate. It is no surprise that functional verification becomes a major bottleneck in the time-to-market of a product. In fact, literature has reported that 70% of design time is spent on making sure the design is bug-free and operating correctly. One of the core verification tasks in achieving high quality products is equivalence checking. Essentially, equivalence checking ensures the preservation of optimized product's functionality to the unoptimized model. This is important for industry because the products are modified constantly to meet different goals such as low power, high performance, etc. The mainstream in conducting equivalence checking includes simulation and formal verification. In simulation approach, golden design and design under verification (DUV) are fed with same stimuli for input expecting outputs to produce identical responses. In case of discrepancy, traces will be generated and DUV will undergo modifications. With the increase in input pins and state elements in designs, exhaustive simulation becomes infeasible. Hence, the completeness of the approach is not guaranteed and notions of coverage has to be accompanied. On the other hand, formal verification incorporates mathematical proofs and guarantee the completeness over the search space. However, formal verification has problems of its own in which it is usually resource intensive. In addition, not all design can be verified after optimization processes. That is to say the golden model and DUV are vastly different in structure which cause modern checker to give inconclusive result. Due to this nature, this thesis focuses in improving the strength and the efficiency of sequential equivalence checking (SEC) using formal approach. While there has been great strides made in the verification for combinational circuits, SEC still remains rather rudimentary. Without powerful SEC as a backbone, aggressive sequential synthesis and optimization are often avoided if the optimized design cannot be proved to be equivalent to the original one. In an attempt to take on the challenges of SEC, we propose two frameworks that successfully determining equivalence for hard-to-verify circuits. The first framework utilizes arbitrary relations between any two nodes within the two sequential circuits in question. The two nodes can reside in the same or across the circuits; likewise, they can be from the same time-frame or across time-frames. The merit for this approach is to use global structure of the circuits to speed up the verification process. The second framework introduces techniques to identify subset but yet powerful multi-node relations (involve more than 2 nodes) which then help to prune large don't care search space and result in a successful SEC framework. In contrast with previous approaches in which exponential number of multi-node relations are mined and learned, we alleviate the computation cost by selecting much fewer invariants to achieve desired conclusion. Although independent, the two frameworks could be used in sequential to complement each other. Experimental results demonstrate that our frameworks can take on many hard-to-verify cases and show a significant speed up over previous approaches. / Master of Science

Mathematical equivalence is crucial throughout the entire course of education. Understanding the concept is a prerequisite for comprehending mathematics, especially in algebra. Despite this, research indicates that many students lack a relational understanding of the concept, both early in their educational journey and as they progress through the grades. However, certain studies suggest that students can demonstrate relational understanding, even at younger ages, as long as you don’t use linguistic assessment methods. This study focuses on primary school students and their understanding of mathematical equivalence. The aim of the study is to investigate whether third-grade students possess a relational understanding of equivalence and, if so, to explore its characteristics. To examine this, a survey was used with math tasks to assess students at a school in southern Sweden’s understanding of equivalence. The surveys have been analyzed through radical constructivism and the Mathematical Equivalence Assesment model. The results indicate that a significant portion of students exhibit partial or complete relational understanding of equality. Furthermore, the findings reveal that students lacking an understanding of the definition of mathematical equivalence attain considerably lower results compared to those with such an understanding. An overarching conclusion that can be drawn in relation to the study's results is that a relational understanding of mathematical equivalence is crucial for long-term learning in mathematics.

Tesis por compendio / A pesar de los enormes beneficios potenciales que ofrecen los cítricos genéticamente modificados (GM), su liberación en campo suscita preocupaciones acerca de su potencial impacto ambiental y posibilidad de que muestren efectos deletéreos inesperados desde un punto de vista agronómico. Las principales preocupaciones que plantea el uso de la transformación genética para la mejora de este cultivo de vida larga, propagación vegetativa y compleja biología reproductiva son: (1) la transferencia de los transgenes vía polen a variedades compatibles de especies de Citrus y afines; (2) la estabilidad de los transgenes a largo plazo; (3) la aparición de efectos pleiotrópicos adversos derivados de la integración y la expresión de los transgenes sobre las principales características agronómicas y fenotípicas del cultivo. Todas estas cuestiones han sido ampliamente estudiadas en otros cultivos anuales GM que ya son o no comerciales. Sin embargo, puesto que el empleo de la transformación genética en la mejora de árboles frutales todavía se encuentra en sus inicios, actualmente se dispone de muy poca información al respecto para estos cultivos. Por todo ello, el futuro de los arboles transgénicos en el ámbito comercial permanece aún incierto, aunque actualmente se dispone de la tecnología para producirlos. Por otro lado, en el caso concreto de los cítricos, no existen variedades transgénicas comerciales ni evidencias inequívocas de que esta herramienta sea realmente útil para afrontar con éxito objetivos de mejora concretos. Lograr cumplir objetivos de mejora tan importantes como la mejora de la calidad nutri-funcional de los frutos cítricos mediante ingeniería genética podría contribuir a una mayor aceptación de esta tecnología por parte del público, puesto que se trata de una mejora dirigida primeramente al consumidor. En este trabajo nos hemos planteado afrontar parte de los aspectos que en gran medida limitan la aceptación y comercialización de cítricos GM, mediante (1) la realización de un experimento de campo con cítricos GM para evaluar su seguridad ambiental y la ausencia de efectos agronómicos adversos (2) el abordaje de un objetivo de mejora de la calidad nutri-funcional de la naranja concreto mediante ingeniería metabólica con la finalidad de reforzar sus propiedades saludables. El experimento de campo consistió en una plantación de cítricos transgénicos que portaban únicamente los genes marcadores uidA y nptII cuya finalidad fue estudiar la viabilidad de la transformación genética en la mejora de genotipos cítricos comercialmente importantes. Este huerto experimental nos sirvió para estimar la frecuencia máxima de dispersión de los transgenes por polen bajo condiciones de polinización abierta y estudiar los factores ambientales, genéticos y fenológicos que la determinan, para así poder proponer medidas de contención apropiadas en futuras plantaciones de cítricos GM. También sirvió como primera aproximación para abordar cuestiones básicas como el estudio de la estabilidad de la expresión de los transgenes a largo plazo (tras 7 años de establecimiento en campo) bajo condiciones reales de cultivo y su potencial impacto sobre la morfología, fenología y calidad de la fruta de los cítricos transgénicos. Los estudios realizados, aunque no resuelven todas las preocupaciones concernientes a los cítricos GM, aportan información crucial relativa a su seguridad y comportamiento en campo, inexistente hasta el momento, que puede servir como base para futuros ensayos de campo con cítricos GM y como guía para las políticas de regulación de su plantación (caso-a-caso). Por otro lado, en este trabajo se ha logrado desarrollar una estrategia para inducir producción temprana de fruta e incrementar el contenido de b-caroteno (pro-vitamina A, con elevada capacidad antioxidante) en la pulpa de una variedad de naranjo dulce mediante ingeniería metabólica. Dicha estrategia consistió en el silenciamiento mediado por RNAi del gen de una β-caroteno hidroxilasa de naranjo (CsβCHX), implicada en la conversión de b-caroteno en xantofilas, combinado con la sobreexpresión del gen FLOWERING LOCUS T de naranjo (CsFT) en plantas transgénicas juveniles de naranjo dulce cv Pineapple. Posteriores ensayos con el animal modelo Caenorhabditis elegans demostraron que la naranjas enriquecidas ejercían un efecto antioxidante in vivo un 20% mayor que las naranjas control isogénicas. Este es el primer ejemplo exitoso de ingeniería metabólica para incrementar el contenido de β-caroteno (o cualquier fitonutriente) en naranjas y demuestra el potencial que tiene la ingeniería genética para el enriquecimiento nutricional de cultivos frutales leñosos. / Pons Bayarri, EA. (2014). Towards application of genetic engineering in citriculture: 1) assessing dispersal, long-term stability and phenotypic impact of transgenes in citrus trees and 2) improving nutri-functional quality of orange fruit through metabolic engineering [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/43588 / Compendio

Current interest in cover cropping is focused on enhancing ecosystem services beyond soil conservation. Cover crop (CC) species function uniquely in their effects on ecosystem services when grown in monoculture or mixtures. This research integrated field experiments and a literature synthesis to evaluate the role of cover crops in improving nitrogen (N) management and simultaneously providing multiple ecosystem services. Legume CC fertilized with poultry litter (PL) could replace 101 to 117 kg N ha-1 of fertilizer in corn (Zea mays L.) production. Rye (Secale cereale L.) CC fertilized with PL had a negligible effect on corn production. Biculture fertilizer equivalence ranged between -12 to +75 kg N ha-1. Fertilizer equivalence of legume-containing treatments increased across time. Without CC, fall-applied PL failed to supply N to corn. Ecosystem services of CC and PL illustrate complex species functions. Bicultures produced more total biomass than monocultures in year 1 but less than rye in year 2. Bicultures were as effective in suppressing weeds as rye, produced corn yield similar to legume, and by the second year had similar amounts of available soil N as the legume. Poultry litter effects and interspecific effects cover crop species biomass differed. Rye yield increased, while legume yield decreased slightly in biculture. Poultry litter increased legume N content and a decrease in legume C:N, while rye N content and C:N were unaffected. The synthesis corroborates that mixed and biculture cover crops yield more than the individual component species. Overyielding was transgressive in 60% of cases studied. Mixture effects varied by species: rye and brassica yield increased, while legume decreased in mixtures. The effect of mixed CC on crop yields varied by crop species and management practices, though generally crops increased 8 to 18% overall. This work can be applied to the design of complex CC and PL systems that optimize individual species functions to enhance ecosystem services. / Ph. D. / Current interest in cover cropping is focused on enhancing ecosystem services beyond soil conservation. Cover crop (CC) species function uniquely in their effects on ecosystem services when grown in monoculture or mixtures. This research integrated field experiments and a literature synthesis to evaluate the role of cover crops in improving nitrogen (N) management and simultaneously providing multiple ecosystem services. Legume CC fertilized with poultry litter (PL) could replace almost half of the inorganic fertilizer required by spring corn (<i>Zea mays</i> L.) production. Rye (<i>Secale cereale</i> L.) CC fertilized with PL had a negligible effect on corn production. Fertilizer equivalence of legume-containing treatments increased across time. Without CC, fall-applied PL failed to supply N to corn. Bicultures produced more total biomass than monocultures in year 1 but less than rye in year 2. Bicultures were as effective in suppressing weeds as rye, produced corn yield similar to legume, and by the second year had similar amounts of available soil N as the legume. Poultry litter effects and interspecific effects cover crop species biomass differed as well. Rye yield increased, while legume yield decreased slightly in biculture. Poultry litter increased legume N content and a decrease in legume C:N, while rye N content and C:N were unaffected. The synthesis corroborates that mixed and biculture cover crops yield more than the individual component species. Mixture effects varied by species: rye and brassica yield increased, while legume decreased in mixtures. The effect of mixed CC on crop yields varied by crop species and management practices, though generally crops increased 8 to 18% overall. This work can be applied to the design of complex CC and PL systems that optimize individual species functions to enhance ecosystem services.

Les nouvelles technologies jouent un rôle croissant dans notre société. Le droit s’est interrogé sur la façon de rendre possible l’utilisation du support électronique dans un monde où seule l’utilisation du support papier était possible jusqu’à peu. L’objectif était d’éviter que la loi par son attachement au support papier n’entrave l’utilisation des nouvelles technologies et plus largement le développement des échanges en ligne. Dans ce contexte, la Commission des Nations Unies pour le Développement du Commerce International (CNUDCI) a développé les principes de neutralité technologique et d’équivalence fonctionnelle aux termes desquels les écrits électroniques sont considérés comme équivalents à ceux papiers s’ils sont en mesure d’endosser les mêmes fonctions que ces derniers. Le législateur français, s’inspirant des travaux de la CNUDCI, a modifié sa législation pour permettre la reconnaissance de la valeur juridique des actes passés par voie électronique. La reconnaissance de la valeur juridique des actes conclus par voie électronique laisse cependant subsister certaines questions relatives la protection du consentement de celui qui contracte en ligne. Le législateur français a ainsi élaboré des règles formalistes et dérogatoires au droit commun concernant la conclusion des contrats électroniques pour protéger le consommateur en ligne. / New technologies play a growing role in the modern world. Some concerns have therefore been raised to determine how to enable the legal use of electronic paper where until recently, only paper support had existed. The main role of such concerns was to avoid that the existing regulations might prejudice development of new technologies (and in a broader way, of online exchange) because only paper support was taken into account. In this context, the United Nations Commission on International Trade Law (UNCITRAL) has developed the principles of technological neutrality and functional equivalence. Pursuant to those principles, electronic writing is considered as equivalent to paper writing as long as the same functions are maintained. The French legislator has sought inspiration in the works of the UNCITRAL to modify the French regulations regarding electronic support. Despite this recognition, some issues remain pending, especially regarding protection of the consent for the online contractor. In this respect, the French legislator has established formalist rules and rules that constitute exception to ordinary law.

Les nouvelles technologies jouent un rôle croissant dans notre société. Le droit s’est interrogé sur la façon de rendre possible l’utilisation du support électronique dans un monde où seule l’utilisation du support papier était possible jusqu’à peu. L’objectif était d’éviter que la loi par son attachement au support papier n’entrave l’utilisation des nouvelles technologies et plus largement le développement des échanges en ligne. Dans ce contexte, la Commission des Nations Unies pour le Développement du Commerce International (CNUDCI) a développé les principes de neutralité technologique et d’équivalence fonctionnelle aux termes desquels les écrits électroniques sont considérés comme équivalents à ceux papiers s’ils sont en mesure d’endosser les mêmes fonctions que ces derniers. Le législateur français, s’inspirant des travaux de la CNUDCI, a modifié sa législation pour permettre la reconnaissance de la valeur juridique des actes passés par voie électronique. La reconnaissance de la valeur juridique des actes conclus par voie électronique laisse cependant subsister certaines questions relatives la protection du consentement de celui qui contracte en ligne. Le législateur français a ainsi élaboré des règles formalistes et dérogatoires au droit commun concernant la conclusion des contrats électroniques pour protéger le consommateur en ligne. / New technologies play a growing role in the modern world. Some concerns have therefore been raised to determine how to enable the legal use of electronic paper where until recently, only paper support had existed. The main role of such concerns was to avoid that the existing regulations might prejudice development of new technologies (and in a broader way, of online exchange) because only paper support was taken into account. In this context, the United Nations Commission on International Trade Law (UNCITRAL) has developed the principles of technological neutrality and functional equivalence. Pursuant to those principles, electronic writing is considered as equivalent to paper writing as long as the same functions are maintained. The French legislator has sought inspiration in the works of the UNCITRAL to modify the French regulations regarding electronic support. Despite this recognition, some issues remain pending, especially regarding protection of the consent for the online contractor. In this respect, the French legislator has established formalist rules and rules that constitute exception to ordinary law.

Ma thèse se situe à l'intersection de \textit {la théorie des groupes géométrique} et \textit{la théorie des groupes mesurée}. Une question majeure dans la théorie des groupes géométrique est d'étudier la classe de quasi-isométrie (QI) et la classe d'équivalence mesurée (ME) d'un groupe, respectivement. $L^p$-équivalence mesurée est une relation d'équivalence qui est définie en ajoutant des contraintes géométriques avec d'équivalence mesurée. En plus, QI est une condition géométrique. Il est une question naturelle, si deux groupes sont QI et ME, si elles sont $L^p$-ME pour certains $p>0$. Dans mon premier article, en collaboration avec R. Tessera, nous répondons négativement à cette question pour $p\geq 1$, montrant que l'extension centrale canonique d'un groupe surface de genre plus élevé ne sont pas $L^1$-ME pour le produit direct de ce groupe de surface avec $\mathbb{Z}$ (alors qu'ils sont à la fois quasi-isométrique et équivalente mesurée).Dans mon deuxième papier, j'ai observé un lien général entre la géométrie des expandeurs, defini comme une séquence des quotients finis ( l'espace de boîte) d'un groupe finiment engendré, et les propriétés mesurée theorique du groupe. Plus précisément, je l'ai prouvé que si deux <<espaces de boîte>> sont quasi-isométrique, les groupes correspondants doivent être <<mesurée équivalente uniformément >>, une notion qui combine à la fois QI et ME. Je prouve aussi une version de ce résultat pour le plongement grossière, ce qui permet de distinguer plusieurs classe des expandeurs. Par exemple, je montre que les expandeurs associé à $SL(m, \mathbb{Z})$ ne grossièrement plongent à les expandeurs associés à $SL_n(\mathbb{Z})$ si $m>n$. / My thesis lies at the intersection of \textit{geometric group theory} and \textit{measured group theory}. A major question in geometric group theory is to study the quasi-isometry (QI) class and the measure equivalence (ME) class of a group, respectively. $L^p$-measure equivalence is an equivalence relation which is defined by adding some geometric constraints with measure equivalence. Besides, quasi-isometry is a geometric condition. It is a natural question if two groups are QI and ME, whether they are $L^p$-ME for some $p>0$. In my first paper, together with R. Tessera, we answer this question negatively for $p\geq 1$, showing that the canonical central extension of a surface group of higher genus is not $L^1$-ME to the direct product of this surface group with $\mathbb{Z}$ (while they are both quasi-isometric and measure equivalent). In my second paper, I observed a general link between the geometry of expanders arising as a sequence of finite quotients (box space) of a finitely generated group, and the measured theoretic properties of the group. More precisely, I proved that if two box spaces' are quasi-isometric, then the corresponding groups must be `uniformly measure equivalent', a notion that combines both quasi-isometry and measure equivalence. I also prove a version of this result for coarse embedding, allowing to distinguish many classes of expanders. For instance, I show that the expanders associated to $SL(m,\mathbb{Z})$ do not coarsely embed inside the expanders associated to $SL_n(\mathbb{Z}$ if $m>n$.