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.
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This book treats a cellular automation as a model of algorithmic-oriented architectures for array data processing. Such an approach motivates the extension of the classical concept of Cellular Automation to Parallel Substitution Algorithm (PSA) in order to fit the potentialities of microelectronics and optics. In this way the following problems of designing cellular architectures are solved: mapping a PSA into a cellular array, space-time, space-space (2D fi 3D) and local-global equivalent transformations of PSAs, composition and decomposition of PSAs, as well as the validity of cellular computations in synchronous and asynchronous modes.
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