This thesis aims at developing strategies to enhance the power of sequential computation and distributed systems, particularly, it deals with sequential break down of operations and decentralized collaborative editing systems. The rapid growth in the use of modern computer technology increases the demand for higher performance in all areas of computing. This demand for ever greater performance led to growth in hardware performance and architecture evolution that results a stress on compiler technology and research community. Since a high-performance microprocessor is at the heart of every general-purpose computer, from servers, to desktop and laptop PCs, to cell-phone platforms such as the iPhone. Therefore increasing the performance is considered to be a permanent challenge in computer science. Similarly, rapid development of computer network inspired the advancement of real-time collaborative editing. Real-time Collaborative Editors (RCE) enable group of users to edit simultaneously shared document from physically dispersed sites that are interconnected by computer network. In such distributed systems, one of the challenges is to avoid from communication conflicts. For this purpose indexed communication acts as an essential requirement. In this thesis, a precision control indexing method is introduced that enables to generate unique identifiers which are used for indexed communication in distributed systems, particularly, in decentralized collaborative editing systems. These identifiers are still real numbers with a specific controlled pattern of precision. Set of identifiers is kept finite that makes it possible to compute local as well as global cardinality. This property plays important role in dealing with indexed communication. Besides this, some other properties including order preservation are observed. The indexing method is tested and verified by experimentation successfully and it leads to design decentralized collaborative editing system. Dealing with sequential break down of operations, we explore limitations of the existing strategies, extended the idea by introducing new strategies. These strategies lead towards optimization (processor, compiler, memory, code). This style of decomposition attracts research communities for further investigation and practical implementation that could lead towards designing an arithmetic unit.
