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Algebraic Decomposition Models for Digital System Design Debugging by Simulation 
 


Authors 
 Zelenko G.V. 
 Ivannikov A.D. 
 Roschin A.V. 
 Stempkovsky A.L. 
Date of publication 
 2016 

Abstract 
 The task of digital systems project debugging by simulation is formulated on the basis of using a family of stationary dynamical systems as a model. Due to the complexity and large dimensions of the task decomposition methods are proposed. The following methods are described and examined: vertical and horizontal structure decomposition, functional decomposition, decomposition based on error types.
Vertical structure decomposition method assumed using a series of simulation levels, each with different variables describing the debagging system. As examples of levels hardware logical simulation or hardware architectural simulation could be considered. Another example is different levels of software simulation. Horizontal structure decomposition assumes the simulation of hardware blocks on different levels and after that the simulation of interactions between blocks. Functional decomposition could be used for digital systems which fulfill the sequence of a finite set of operations. In such a case it is possible to simulate the fulfillment of each operation separately with any degree of accuracy and then to check the correctness of their sequencing fulfillment. Decomposition based on error types assumes the simulation on definite level which is most suitable for some error type detecting. Rather often two or more decomposition methods are used simultaneously.
The concept of an operator upon digital system memory is formally introduced on the algebraic approach bases. The concept of a generalized memory consisting of memory cells, register contents, active operator label and current time value is introduced. An operator functioning upon generalized memory is formalized. Structural analysis of an operator domain and operator range is fulfilled. The definition of operator’s product is introduced, the condition of such a product existence is analyzed. It is shown that any digital system software is the product of operators, operator set is a semi group. The developed formal model is supposed to be used for the creation of digital systems software test generation. 
Keywords 
 complex digital system model, debugging by computer simulation, system on a chip design, logical simulation, logicotiming analysis, algebraic models, algebraic model for software, program as a semi group of operators. 
Library reference 
 Zelenko G.V., Ivannikov A.D., Roschin A.V., Stempkovsky A.L. Algebraic Decomposition Models for Digital System Design Debugging by Simulation // Problems of Perspective Micro and Nanoelectronic Systems Development  2016. Proceedings / edited by A. Stempkovsky, Moscow, IPPM RAS, 2016. Part 3. P. 232239. 
URL of paper 
 http://www.mesconference.ru/data/year2016/pdf/D199.pdf 

