Overview

Parallel Substitution Algorithm (PSA) is a new model for distributed (cellular) computations. It provides a concise mapping of distributed computation processes into cellular arrays. A PSA is specified by a set of parallel substitutions operating over a cellular array.Two concepts make PSA a powerful tool for modelling cellular computations: 1) naming functions which allow the specification of any type of interactions in the computation space, 2) a context which serves to represent control of a computational process in time.The foundation of PSA theory comprises validity conditions of computations in the synchronous and asynchronous modes, space-time, space-space (2D 3D) and global-local equivalent transformations of PSAs, composition and decomposition of PSAs and interpretation of PSAs with automata nets.On the basis of the PSA theory, a variety of tools and techniques is developed for designing algorithmic-oriented cellular VLSI and optical architectures.Contents: Parallel Substitution Algorithm: Basic Notions and DefinitionsPSA Subclasses and ExtensionsInterpretation of Stationary PSAs by Automata Nets Validity of Parallel Substitution Systems: Synchronous and Asynchronous Modes of Execution of Parallel Substitution SystemsValidity Conditions of Parallel Substitution SystemsCorrectness of PSSs with Substitutions of Different Execution Times Asynchronous Composition of Parallel Substitution Algorithms: Two Types of Parallel Asynchronous CompositionValidity of Asynchronous Composition of PSAsConstruction of Composed PSAs Equivalent Transformations of PSAs: 2D 3D PSA TransformationSynchronous Asynchronous Transformation of PSAs, Space Time Transformation of PSAs PSA Application to Cellular Architecture Design: Computer Simulation of Cellular ComputationsPSAs and Architectures of 2D Cellular Processors, PSAs and Architectures of 3D Cellular ProcessorsReadership: Researchers and postgraduate students in computer science and designers of parallel computer architecture.

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