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 Ž 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 Definitions
• PSA Subclasses and Extensions
• Interpretation of Stationary PSAs by Automata Nets
• Validity of Parallel Substitution Systems:
• Synchronous and Asynchronous Modes of Execution of Parallel Substitution Systems
• Validity Conditions of Parallel Substitution Systems
• Correctness of PSSs with Substitutions of Different Execution Times
• Asynchronous Composition of Parallel Substitution Algorithms:
• Two Types of Parallel Asynchronous Composition
• Validity of Asynchronous Composition of PSAs
• Construction of Composed PSAs
• Equivalent Transformations of PSAs:
• 2D ® 3D PSA Transformation
• Synchronous–Asynchronous Transformation of PSAs, Space–Time Transformation of PSAs
• PSA Application to Cellular Architecture Design:
• Computer Simulation of Cellular Computations, PSAs and Architectures of 2D Cellular Processors, PSAs and Architectures of 3D Cellular Processors