M.A. (African Languages) / Please refer to full text to view abstract

In the late 20th century the reliable and efficient transmission, reception and storage of information proved to be central to the most successful economies all over the world. The Internet, once a classified project accessible to a selected few, is now part of the everyday lives of a large part of the human population, and as such the efficient storage of information is an important part of the information economy. The improvement of the information storage density of optical and electronic media has been remarkable, but the elimination of redundancy in stored data and the reliable reconstruction of the original data is still a desired goal. The field of source coding is concerned with the compression of redundant data and its reliable decompression. The arithmetic source code, which was independently proposed by J. J. Rissanen and R. Pasco in 1976, revolutionized the field of source coding. Compression algorithms that use an arithmetic code to encode redundant data are typically more effective and computationally more efficient than compression algorithms that use earlier source codes such as extended Huffman codes. The arithmetic source code is also more flexible than earlier source codes, and is frequently used in adaptive compression algorithms. The arithmetic code remains the source code of choice, despite having been introduced more than 30 years ago. The problem of effectively encoding data from sources with known statistics (i.e. where the probability distribution of the source data is known) was solved with the introduction of the arithmetic code. The probability distribution of practical data is seldomly available to the source encoder, however. The source coding of data from sources with unknown statistics is a more challenging problem, and remains an active research topic. Enumerative source codes were introduced by T. J. Lynch and L. D. Davisson in the 1960s. These lossless source codes have the remarkable property that they may be used to effectively encode source sequences from certain sources without requiring any prior knowledge of the source statistics. One drawback of these source codes is the computationally complex nature of their implementations. Several years after the introduction of enumerative source codes, J. G. Cleary and I. H. Witten proved that approximate enumerative source codes may be realized by using an arithmetic code. Approximate enumerative source codes are significantly less complex than the original enumerative source codes, but are less effective than the original codes. Researchers have become more interested in arithmetic source codes than enumerative source codes since the publication of the work by Cleary and Witten. This thesis concerns the original enumerative source codes and their use in Burrows–Wheeler compression algorithms. A novel implementation of the original enumerative source code is proposed. This implementation has a significantly lower computational complexity than the direct implementation of the original enumerative source code. Several novel enumerative source codes are introduced in this thesis. These codes include optimal fixed–to–fixed length source codes with manageable computational complexity. A generalization of the original enumerative source code, which includes more complex data sources, is proposed in this thesis. The generalized source code uses the Burrows–Wheeler transform, which is a low–complexity algorithm for converting the redundancy of sequences from complex data sources to a more accessible form. The generalized source code effectively encodes the transformed sequences using the original enumerative source code. It is demonstrated and proved mathematically that this source code is universal (i.e. the code has an asymptotic normalized average redundancy of zero bits). AFRIKAANS : Die betroubare en doeltreffende versending, ontvangs en berging van inligting vorm teen die einde van die twintigste eeu die kern van die mees suksesvolle ekonomie¨e in die wˆereld. Die Internet, eens op ’n tyd ’n geheime projek en toeganklik vir slegs ’n klein groep verbruikers, is vandag deel van die alledaagse lewe van ’n groot persentasie van die mensdom, en derhalwe is die doeltreffende berging van inligting ’n belangrike deel van die inligtingsekonomie. Die verbetering van die bergingsdigteid van optiese en elektroniese media is merkwaardig, maar die uitwissing van oortolligheid in gebergde data, asook die betroubare herwinning van oorspronklike data, bly ’n doel om na te streef. Bronkodering is gemoeid met die kompressie van oortollige data, asook die betroubare dekompressie van die data. Die rekenkundige bronkode, wat onafhanklik voorgestel is deur J. J. Rissanen en R. Pasco in 1976, het ’n revolusie veroorsaak in die bronkoderingsveld. Kompressiealgoritmes wat rekenkundige bronkodes gebruik vir die kodering van oortollige data is tipies meer doeltreffend en rekenkundig meer effektief as kompressiealgoritmes wat vroe¨ere bronkodes, soos verlengde Huffman kodes, gebruik. Rekenkundige bronkodes, wat gereeld in aanpasbare kompressiealgoritmes gebruik word, is ook meer buigbaar as vroe¨ere bronkodes. Die rekenkundige bronkode bly na 30 jaar steeds die bronkode van eerste keuse. Die probleem om data wat afkomstig is van bronne met bekende statistieke (d.w.s. waar die waarskynlikheidsverspreiding van die brondata bekend is) doeltreffend te enkodeer is opgelos deur die instelling van rekenkundige bronkodes. Die bronenkodeerder het egter selde toegang tot die waarskynlikheidsverspreiding van praktiese data. Die bronkodering van data wat afkomstig is van bronne met onbekende statistieke is ’n groter uitdaging, en bly steeds ’n aktiewe navorsingsveld. T. J. Lynch and L. D. Davisson het tel–bronkodes in die 1960s voorgestel. Tel– bronkodes het die merkwaardige eienskap dat bronsekwensies van sekere bronne effektief met hierdie foutlose kodes ge¨enkodeer kan word, sonder dat die bronenkodeerder enige vooraf kennis omtrent die statistieke van die bron hoef te besit. Een nadeel van tel–bronkodes is die ho¨e rekenkompleksiteit van hul implementasies. J. G. Cleary en I. H. Witten het verskeie jare na die instelling van tel–bronkodes bewys dat benaderde tel–bronkodes gerealiseer kan word deur die gebruik van rekenkundige bronkodes. Benaderde tel–bronkodes het ’n laer rekenkompleksiteit as tel–bronkodes, maar benaderde tel–bronkodes is minder doeltreffend as die oorspronklike tel–bronkodes. Navorsers het sedert die werk van Cleary en Witten meer belangstelling getoon in rekenkundige bronkodes as tel–bronkodes. Hierdie tesis is gemoeid met die oorspronklike tel–bronkodes en die gebruik daarvan in Burrows–Wheeler kompressiealgoritmes. ’n Nuwe implementasie van die oorspronklike tel–bronkode word voorgestel. Die voorgestelde implementasie het ’n beduidende laer rekenkompleksiteit as die direkte implementasie van die oorspronklike tel–bronkode. Verskeie nuwe tel–bronkodes, insluitende optimale vaste–tot–vaste lengte tel–bronkodes met beheerbare rekenkompleksiteit, word voorgestel. ’n Veralgemening van die oorspronklike tel–bronkode, wat meer komplekse databronne insluit as die oorspronklike tel–bronkode, word voorgestel in hierdie tesis. The veralgemeende tel–bronkode maak gebruik van die Burrows–Wheeler omskakeling. Die Burrows–Wheeler omskakeling is ’n lae–kompleksiteit algoritme wat die oortolligheid van bronsekwensies wat afkomstig is van komplekse databronne omskakel na ’n meer toeganklike vorm. Die veralgemeende bronkode enkodeer die omgeskakelde sekwensies effektief deur die oorspronklike tel–bronkode te gebruik. Die universele aard van hierdie bronkode word gedemonstreer en wiskundig bewys (d.w.s. dit word bewys dat die kode ’n asimptotiese genormaliseerde gemiddelde oortolligheid van nul bisse het). Copyright / Dissertation (MEng)--University of Pretoria, 2010. / Electrical, Electronic and Computer Engineering / unrestricted

Reusing code can expedite software creation, analysis and exploration of data. Expediency can be particularly valuable for users of computational notebooks, where duplication allows them to quickly test hypotheses and iterate over data, without creating code from scratch. In this thesis, I’ll explore the topic of code duplication and the behaviour of code reuse for Jupyter notebooks; quantifying and describing snippets of code and explore potential barriers for reuse. As part of this thesis I conducted two studies into Jupyter notebooks use. In my first study, I mined GitHub repositories, quantifying and describing code duplicates contained within repositories that contained at least one Jupyter notebook. For my second study, I conducted an observational user study using a contextual inquiry, where my participants solved specific tasks using notebooks, while I observed and took notes. The work in this thesis can be categorized as exploratory, since both my studies were aimed at generating hypotheses for which further studies can build upon. My contributions with this thesis is two-fold: a thorough description of code duplicates contained within GitHub repositories and an exploration of the behaviour behind code reuse in Jupyter notebooks. It is my desire that others can build upon this work to provide new tools, addressing some of the issues outlined in this thesis. / Graduate

The use of AI tools for code generation is increasing in popularity, and two of these tools are ChatGPT and GitHub Copilot. These tools could potentially reduce development time and costs for developers and companies, however, ensuring the correctness and quality of AI-generated code is crucial for its adoption. This study conducted a quantitative controlled experiment to evaluate the code generation capabilities of Copilot and ChatGPT in terms of code correctness and quality. The experiment aimed to address research questions regarding the performance of these AI tools. The results indicate that both ChatGPT and Copilot can generate correct code from given instructions, though there is room for improvement. ChatGPT achieved a correctness rate of 87.33%, while Copilot performed slightly better at 89%. Statistical analysis revealed no significant difference in code correctness between the two tools. Regarding code quality, ChatGPT demonstrated impressive performance, with 98.52% of generated lines free from quality rule violations. Furthermore, 80.7% of ChatGPT-generated algorithms had no quality rule violations. Copilot generated correct lines for 94.07% of total lines but only achieved 64.7% of algorithms with no quality rule violations. The statistical analysis showed a statistically significant difference in code quality between ChatGPT and Copilot, indicating that ChatGPT generally produces higher quality code. This research contributes to understanding the capabilities of AI code generation tools and highlights their potential to produce correct and high-quality code.

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Expander codes are sparse graph-based codes with good decoding algorithms. We present a linear-time decoding algorithm for (C,D, alpha, gamma) expander codes based on graphs with any expansion factor given that the minimum distances of the inner codes are bounded below. We also design graph-based codes with hierarchical locality. Such codes provide tiered recovery, depending on the number of erasures. A small number of erasures may be handled by only accessing a few other symbols, allowing for small locality, while larger number may involve a greater number of symbols. This provides an alternative to requiring disjoint repair groups. We also consider availability in this context, relying on the interplay between inner codes and the Tanner graph. We define new families of algebraic geometry codes for the purpose of code-based cryptography. In particular, we consider twisted Hermitian codes, twisted codes from a quotient of the Hermitian curve; and twisted norm-trace codes. These codes have Schur squares with large dimensions and hence could be considered as potential replacements for Goppa codes in the McEliece cryptosytem. However, we study the code-based cryptosystem based on twisted Hermitian codes and lay foundations for a potential attack on such a cryptosystem. / Doctor of Philosophy / Coding theory finds applications in various places such as data transmission, data storage, and even post-quantum cryptography. The goal of data transmission is to ensure fast and efficient information transfer. It is ideal to correct maximum number of errors introduced during transmission by noisy channels. We provide a new construction of expander codes (graph-based codes) and provide a linear-time decoding algorithm which corrects a constant-fraction of errors for these codes given any expansion factor. In this context, channel noise causes distortion of symbols, so that received symbols may be different than those originally sent. We are also interested in codes for erasure recovery, meaning those which restore missing symbols. A recent technique to recover the sent messages is by accesing a small subset of this received information, called locality. We analyze the locality properties of Tanner codes equipped with specific inner code. Code-based cryptography is a leading candidate in the post-quantum setting, meaning it is believed to be secure against quantum algorithms. The McEliece cryptosystem in which the underlying code is a Goppa code is popularly studied and is a top candidate in the NIST competition. However, the adoption of this system is not immediate due to its large key sizes. Code-based cryptosystems based on codes other than Goppa codes might provide a solution. We provide constructions of a new family of codes, called twisted algebraic geomtery codes which may provide alternatives of Goppa codes in the McEliece cryptosystem.

The development of high integrity embedded systems remains an arduous and error-prone task, despite the efforts by researchers in inventing tools and techniques for design automation. Much of the problem arises from the fact that the semantics of the modeling languages for the various tools, are often distinct, and the semantics gaps are often filled manually through the engineer's understanding of one model or an abstraction. This provides an opportunity for bugs to creep in, other than standardizing software engineering errors germane to such complex system engineering. Since embedded systems applications such as avionics, automotive, or industrial automation are safety critical, it is very important to invent tools, and methodologies for safe and reliable system design. Much of the tools, and techniques deal with either the design of embedded platforms (hardware, networking, firmware etc), and software stack separately. The problem of the semantic gap between these two, as well as between models of computation used to capture semantics must be solved in order to design safer embedded systems. In this dissertation we propose a methodology for the end-to-end modeling and analysis of safety-critical embedded systems. Our approach consists of formal platform modeling, and analysis; formal application modeling; and 'correct-by-construction' code synthesis with the aim of bridging semantic gaps between the various abstractions and models required for the end-to-end system design. While the platform modeling language AADL has formal semantics, and analysis tools for real-time, and performance verification, the application behavior modeling in AADL is weak and part of an annex. In our work, we create the APECS (AADL and Polychrony based Embedded Computing Synthesis) methodology to allow an embedded system design specification all the way from platform architecture and platform components, the real-time behavior, non-functional properties, as well as the application software modeling. Our main contribution is to integrate a polychronous application software modeling language, and synthesis algorithms in order for synthesis of the embedded software running on the target platform, with the required constraints being met. We believe that a polychronous approach is particularly well suited for a multiprocessor/multi-controller distributed platform where different components often operate at independent rates and concurrently. Further, the use of a formal polychronous language will allow for formal validation of the software prior to code generation. We present a prototype framework that implements this approach, which we refer to as the AADL and Polychrony based Embedded Computing System (APECS). Our prototype utilizes an extended version of Ocarina to provide code generation for the AADL model. Our polychronous modeling language is MRICDF. Our prototype extends Ocarina to support software specification in MRICDF and generate multi-threaded software. Additionally, we implement an automated translation from Simulink to MRICDF, allowing designers to benefit from its formal semantics and exploit engineers' familiarity with Simulink tools, and legacy models. We present case studies utilizing APECS to implement safety critical systems both natively in MRICDF and in Simulink through automated translation. / Ph. D.

Consider a network which consists of noiseless point to point channels. In this network, the source node wants to send messages to a specific set of sink nodes. If an intermediate node v has just one input channel then the received symbol by that node can be replicated and sent to the outgoing channels from v. If v has at least two incoming channels then it has two options. It can either send the received symbols one-by-one, one symbol in each time unit, or v can transmit a combination of the received symbols. The former choice takes more time compared to the latter option, which is called network coding. In the literature, it has been shown that in a single source finite acyclic network the maximum throughput can be achieved by using linear network codes. Significant effort has been made to efficiently construct good network codes. In addition, a polynomial time algorithm for constructing a linear network code on a given network was introduced. Also an algorithm for constructing a linear multicast code on an acyclic network was introduced. Finally, a method for finding a representation matrix for the network matroid of a given network G was also introduced. This matrix can be used to construct a generic code. In this thesis we first provide a review of some known methods for constructing linear multicast, broadcast and dispersion codes for cyclic and acyclic networks. We then give a method for normalization of a non-normal code, and also give a new algorithm for constructing a linear multicast code on a cyclic network. The construction of generic network codes is also addressed. / Graduate / 0984 / 0544 / esmaeili@uvic.ca

This work deals with problems of the barcode applied to automatic identification. Description of their major part, creation of the bar code online generator, a web-page information system using the barcodes to identify the object, is presented.