A MATHEMATICAL MODEL AND PRODUCT MANAGEMENT SCHEME FOR IMPLEMENTING PARALLEL PRODUCT COMPUTING
Abstract
Relevance. Effective mathematical models for organizing parallel computing utilize principles of simultaneous rule execution on independent data fragments, as well as methods for processing symbolic information as a unifying category for various data types. Production systems in A.A. Markov Jr.'s notation offer the necessary potential for creating such models, but their standard control scheme is sequential, limiting their application in applied problems. Therefore, synthesizing modified production systems and their control schemes aimed at parallelizing the computational process of processing symbolic information is a pressing issue. The goal of this study is to reduce the execution time of a modified production model through bidirectional processing of symbol strings. The solution method is based on the application of principles of bidirectional grammatical parsing from the theory of syntactic analysis and compilation in algorithmic production systems and consists of modifying A.A. Markov's standard production computation scheme. This is achieved by introducing single-shot productions, bidirectional access to the string being processed, decomposing the original system into sections, and introducing a set of guard conditions for conflict resolution. The production model is implemented for typical symbolic processing tasks: word tagging and word reversal. Results. The structure of a modified production system was developed that overcomes the limitation of A.A. Markov's standard scheme—the sequential nature of computations. As a result of the study, a formal model of serial-parallel processing was created, a new control scheme was developed, and the correctness of the computations was demonstrated. Simulation on typical tasks showed a reduction in word processing time by almost half, achieved, in part, by eliminating the mandatory return to the first production in the control scheme and aggregating productions into sections. Conclusion. The study confirmed the feasibility and effectiveness of transforming A.A. Markov's sequential production systems into serial-parallel production models that produce correct results. A promising area of application is methods and software and hardware in homogeneous computing systems for high-performance processing of symbolic information
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