String diagrams provide a convenient graphical framework which may be used for equational reasoning about morphisms of monoidal categories. However, unlike term rewriting, which is the standard way of reasoning about the morphisms of monoidal categories, rewriting string diagrams results in shorter equational proofs, because the string diagrammatic representation allows us to formally establish equalities modulo any rewrite steps which follow from the monoidal structure. Manipulating string diagrams by hand is a time-consuming and error-prone process, especially for large string diagrams. This can be ameliorated by using software proof assistants, such as Quantomatic. However, reasoning about concrete string diagrams may be limiting and in some scenarios it is necessary to reason about entire (infinite) families of string diagrams. When doing so, we face the same problems as for manipulating concrete string diagrams, but in addition, we risk making further mistakes if we are not precise enough about the way we represent (infinite) families of string diagrams. The primary goal of this thesis is to design a mathematical framework for equational reasoning about infinite families of string diagrams which is amenable to computer automation. We will be working with context-free families of string diagrams and we will represent them using context-free graph grammars. We will model equations between infinite families of diagrams using rewrite rules between context-free grammars. Our framework represents equational reasoning about concrete string diagrams and context-free families of string diagrams using double-pushout rewriting on graphs and context-free graph grammars respectively. We will prove that our representation is sound by showing that it respects the concrete semantics of string diagrammatic reasoning and we will show that our framework is appropriate for software implementation by proving important decidability properties.

Thesis (Ph.D.)--Hong Kong University of Science and Technology, 2008. / Includes bibliographical references (p. 120-125). Also available in electronic version.

Thesis (M.Sc.) - Carleton University, 2005. / Includes bibliographical references (p. 61-63). Also available in electronic format on the Internet.

Thesis (MSc)--University of Stellenbosch, 2008. / Bibliography. Also available via the Internet.

Thesis (M. Sc. - Carleton University, 2001. / Includes bibliographical references (p. 138-141). Also available in electronic format on the Internet.

Abstração é um processo que consiste em encontrar similaridades em artefatos e omitir detalhes desnecessários em um particular momento. Em geral, tal processo resulta em simplificação, substituindo situações do mundo real complexas e excessivamente detalhadas por modelos compreensíveis que admitem resolução. Na computação, existem estilos de programação que fornecem ao programador uma visão particular sobre a organização e execução de um programa. Cada estilo viabiliza formas de representação e tratamento de abstrações aderentes ao conjunto de conceitos, valores, percepções e práticas compartilhadas por uma comunidade. Em particular, o fenômeno de reescrita de termos viabiliza transformações entre espaços de abstração. Como instância de tal fenômeno, macros constituem um padrão sintático que especifica uma transformação simbólica ou algorítmica sobre uma sequência de símbolos associada. Na ocorrência de uma instância de tal padrão sintático, este é substituído pela aplicação de sua transformação correspondente. Dada a importância da disponibilização de estruturas de representação mais convenientes às necessidades dos usuários, o objetivo principal desta tese é tratar da utilização de sistemas de reescrita como mecanismos de abstração em transformações textuais. Para tal, técnicas de projeto e aspectos de implementação de tais sistemas são apresentados, com enfoque em macros. / Abstraction is a process of finding similarities in artifacts and omitting unnecessary details at a particular moment. In general, such a process results in simplification, replacing complex and overly detailed real-world situations with understandable models that admit resolution. In computing, there are programming styles that give the programmer a particular insight into the organization and execution of a program. Each style enables forms of representation and treatment of abstractions adhering to the set of concepts, values, perceptions and practices shared by a community. In particular, the term rewriting phenomenon enables transformations along spaces of abstraction. As an instance of such a phenomenon, macros constitute a syntactic pattern that specifies a symbolic or algorithmic transformation over an associated symbol sequence. In the occurrence of an instance, the matched syntactic pattern is replaced by the application of its corresponding transformation. Given the importance of making representation structures more convenient to users\' needs, this thesis aims at addressing the use of rewriting systems as abstraction mechanics in textual transformations. To this end, design techniques and implementation aspects of such systems are presented, focusing on macros.

Abstração é um processo que consiste em encontrar similaridades em artefatos e omitir detalhes desnecessários em um particular momento. Em geral, tal processo resulta em simplificação, substituindo situações do mundo real complexas e excessivamente detalhadas por modelos compreensíveis que admitem resolução. Na computação, existem estilos de programação que fornecem ao programador uma visão particular sobre a organização e execução de um programa. Cada estilo viabiliza formas de representação e tratamento de abstrações aderentes ao conjunto de conceitos, valores, percepções e práticas compartilhadas por uma comunidade. Em particular, o fenômeno de reescrita de termos viabiliza transformações entre espaços de abstração. Como instância de tal fenômeno, macros constituem um padrão sintático que especifica uma transformação simbólica ou algorítmica sobre uma sequência de símbolos associada. Na ocorrência de uma instância de tal padrão sintático, este é substituído pela aplicação de sua transformação correspondente. Dada a importância da disponibilização de estruturas de representação mais convenientes às necessidades dos usuários, o objetivo principal desta tese é tratar da utilização de sistemas de reescrita como mecanismos de abstração em transformações textuais. Para tal, técnicas de projeto e aspectos de implementação de tais sistemas são apresentados, com enfoque em macros. / Abstraction is a process of finding similarities in artifacts and omitting unnecessary details at a particular moment. In general, such a process results in simplification, replacing complex and overly detailed real-world situations with understandable models that admit resolution. In computing, there are programming styles that give the programmer a particular insight into the organization and execution of a program. Each style enables forms of representation and treatment of abstractions adhering to the set of concepts, values, perceptions and practices shared by a community. In particular, the term rewriting phenomenon enables transformations along spaces of abstraction. As an instance of such a phenomenon, macros constitute a syntactic pattern that specifies a symbolic or algorithmic transformation over an associated symbol sequence. In the occurrence of an instance, the matched syntactic pattern is replaced by the application of its corresponding transformation. Given the importance of making representation structures more convenient to users\' needs, this thesis aims at addressing the use of rewriting systems as abstraction mechanics in textual transformations. To this end, design techniques and implementation aspects of such systems are presented, focusing on macros.

Thesis (Ph.D.)--Hong Kong University of Science and Technology, 2007. / Includes bibliographical references (leaves 106-113). Also available in electronic version.

We present a generic proof methodology to automatically prove correctness of design transformations introduced at the Register-Transfer Level (RTL) to achieve lower power dissipation in hardware systems. We also introduce a new algorithm to reduce switching activity power dissipation in microprocessors. We further apply our technique in a completely different domain of dynamic power management of Systems-on-Chip (SoCs). We demonstrate our methodology on real-life circuits. In this thesis, we address the dual problem of transforming hardware systems at higher levels of abstraction to achieve lower power dissipation, and a reliable way to verify the correctness of the afore-mentioned transformations. The thesis is in three parts. The first part introduces Instruction-driven Slicing, a new algorithm to automatically introduce RTL/System level annotations in microprocessors to achieve lower switching power dissipation. The second part introduces Dedicated Rewriting, a rewriting based generic proof methodology to automatically prove correctness of such high-level transformations for lowering power dissipation. The third part implements dedicated rewriting in the context of dynamically managing power dissipation of mobile and hand-held devices. We first present instruction-driven slicing, a new technique for annotating microprocessor descriptions at the Register Transfer Level in order to achieve lower power dissipation. Our technique automatically annotates existing RTL code to optimize the circuit for lowering power dissipated by switching activity. Our technique can be applied at the architectural level as well, achieving similar power gains. We first demonstrate our technique on architectural and RTL models of a 32-bit OpenRISC pipelined processor (OR1200), showing power gains for the SPEC2000 benchmarks. These annotations achieve reduction in power dissipation by changing the logic of the design. We further extend our technique to an out-of-order superscalar core and demonstrate power gains for the same SPEC2000 benchmarks on architectural and RTL models of PUMA, a fixed point out-of-order PowerPC microprocessor. We next present dedicated rewriting, a novel technique to automatically prove the correctness of low power transformations in hardware systems described at the Register Transfer Level. We guarantee the correctness of any low power transformation by providing a functional equivalence proof of the hardware design before and after the transformation. Dedicated rewriting is a highly automated deductive verification technique specially honed for proving correctness of low power transformations. We provide a notion of equivalence and establish the equivalence proof within our dedicated rewriting system. We demonstrate our technique on a non-trivial case study. We show equivalence of a Verilog RTL implementation of a Viterbi decoder, a component of the DRM System-On-Chip (SoC), before and after the application of multiple low power transformations. We next apply dedicated rewriting to a broader context of holistic power management of SoCs. This in turn creates a self-checking system and will automatically flag conflicting constraints or rules. Our system will manage power constraint rules using dedicated rewriting specially honed for dynamic power management of SoC designs. Together, this provides a common platform and representation to seamlessly cooperate between hardware and software constraints to achieve maximum platform power optimization dynamically during execution. We demonstrate our technique in multiple contexts on an SoC design of the state-of-the-art next generation Intel smartphone platform. Finally, we give a proof of instruction-driven slicing. We first prove that the annotations automatically introduced in the OR1200 processor preserve the original functionality of the machine using the ACL2 theorem prover. Then we establish the same proof within our dedicated rewriting system, and discuss the merits of such a technique and a framework. In the context of today's shrinking hardware and mobile internet devices, lowering power dissipation is a key problem. Verifying the correctness of transformations which achieve that is usually a time-consuming affair. Automatic and reliable methods of verification that are easy to use are extremely important. In this thesis we have presented one such transformation, and a generic framework to prove correctness of that and similar transformations. Our methodology is constructed in a manner that easily and seamlessly fits into the design cycle of creating complicated hardware systems. Our technique is also general enough to be applied in a completely different context of dynamic power management of mobile and hand-held devices. / text

Restarting automata were introduced as a model for analysis by reduction which is a linguistically motivated method for checking correctness of a sentence. The thesis studies locally restricted models of restarting automata which (to the contrary of general restarting automata) can modify the input tape based only on a limited context. The investigation of such restricted models is easier than in the case of general restarting automata. Moreover, these models are effectively learnable from positive samples of reductions and their instructions are human readable. Powered by TCPDF (www.tcpdf.org)