A Comprehensive Methodology for Algorithm Characterization, Regularization and Mapping Into Optimal VLSI Arrays.

This dissertation provides a fairly comprehensive treatment of a broad class of algorithms as it pertains to systolic implementation. We describe some formal algorithmic transformations that can be utilized to map regular and some irregular compute-bound algorithms into the best fit time-optimal systolic architectures. The resulted architectures can be one-dimensional, two-dimensional, three-dimensional or nonplanar. The methodology detailed in the dissertation employs, like other methods, the concept of dependence vector to order, in space and time, the index points representing the algorithm. However, by differentiating between two types of dependence vectors, the ordering procedure is allowed to be flexible and time optimal. Furthermore, unlike other methodologies, the approach reported here does not put constraints on the topology or dimensionality of the target architecture. The ordered index points are represented by nodes in a diagram called Systolic Precedence Diagram (SPD). The SPD is a form of precedence graph that takes into account the systolic operation requirements of strictly local communications and regular data flow. Therefore, any algorithm with variable dependence vectors has to be transformed into a regular indexed set of computations with local dependencies. This can be done by replacing variable dependence vectors with sets of fixed dependence vectors. The SPD is transformed into an acyclic, labeled, directed graph called the Systolic Directed Graph (SDG). The SDG models the data flow as well as the timing for the execution of the given algorithm on a time-optimal array. The target architectures are obtained by projecting the SDG along defined directions. If more than one valid projection direction exists, different designs are obtained. The resulting architectures are then evaluated to determine if an improvement in the performance can be achieved by increasing PE fan-out. If so, the methodology provides the corresponding systolic implementation. By employing a new graph transformation, the SDG is manipulated so that it can be mapped into fixed-size and fixed-depth multi-linear arrays. The latter is a new concept of systolic arrays that is adaptable to changes in the state of technology. It promises a bonded clock skew, higher throughput and better performance than the linear implementation

Proceedings of the Caltech Conference on Very Large Scale Integration, held at the California Institute of Technology 22 - 24 January 1979 ; Organized by the Caltech Computer Science Department and the Caltech Industrial Associates Office

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Applications and implementation of neuro-connectionist architectures.

by H.S. Ng.Thesis (M.Phil.)--Chinese University of Hong Kong, 1996.Includes bibliographical references (leaves 91-97).Chapter 1 --- Introduction --- p.1Chapter 1.1 --- Introduction --- p.1Chapter 1.2 --- Neuro-connectionist Network --- p.2Chapter 2 --- Related Works --- p.5Chapter 2.1 --- Introduction --- p.5Chapter 2.1.1 --- Kruskal's Algorithm --- p.5Chapter 2.1.2 --- Prim's algorithm --- p.6Chapter 2.1.3 --- Sollin's algorithm --- p.7Chapter 2.1.4 --- Bellman-Ford algorithm --- p.8Chapter 2.1.5 --- Floyd-Warshall algorithm --- p.9Chapter 3 --- Binary Relation Inference Network and Path Problems --- p.11Chapter 3.1 --- Introduction --- p.11Chapter 3.2 --- Topology --- p.12Chapter 3.3 --- Network structure --- p.13Chapter 3.3.1 --- Single-destination BRIN architecture --- p.14Chapter 3.3.2 --- Comparison between all-pair BRIN and single-destination BRIN --- p.18Chapter 3.4 --- Path Problems and BRIN Solution --- p.18Chapter 3.4.1 --- Minimax path problems --- p.18Chapter 3.4.2 --- BRIN solution --- p.19Chapter 4 --- Analog and Voltage-mode Approach --- p.22Chapter 4.1 --- Introduction --- p.22Chapter 4.2 --- Analog implementation --- p.24Chapter 4.3 --- Voltage-mode approach --- p.26Chapter 4.3.1 --- The site function --- p.26Chapter 4.3.2 --- The unit function --- p.28Chapter 4.3.3 --- The computational unit --- p.28Chapter 4.4 --- Conclusion --- p.29Chapter 5 --- Current-mode Approach --- p.32Chapter 5.1 --- Introduction --- p.32Chapter 5.2 --- Current-mode approach for analog VLSI Implementation --- p.33Chapter 5.2.1 --- Site and Unit output function --- p.33Chapter 5.2.2 --- Computational unit --- p.34Chapter 5.2.3 --- A complete network --- p.35Chapter 5.3 --- Conclusion --- p.37Chapter 6 --- Neural Network Compensation for Optimization Circuit --- p.40Chapter 6.1 --- Introduction --- p.40Chapter 6.2 --- A Neuro-connectionist Architecture for error correction --- p.41Chapter 6.2.1 --- Linear Relationship --- p.42Chapter 6.2.2 --- Output Deviation of Computational Unit --- p.44Chapter 6.3 --- Experimental Results --- p.46Chapter 6.3.1 --- Training Phase --- p.46Chapter 6.3.2 --- Generalization Phase --- p.48Chapter 6.4 --- Conclusion --- p.50Chapter 7 --- Precision-limited Analog Neural Network Compensation --- p.51Chapter 7.1 --- Introduction --- p.51Chapter 7.2 --- Analog Neural Network hardware --- p.53Chapter 7.3 --- Integration of analog neural network compensation of connectionist net- work for general path problems --- p.54Chapter 7.4 --- Experimental Results --- p.55Chapter 7.4.1 --- Convergence time --- p.56Chapter 7.4.2 --- The accuracy of the system --- p.57Chapter 7.5 --- Conclusion --- p.58Chapter 8 --- Transitive Closure Problems --- p.60Chapter 8.1 --- Introduction --- p.60Chapter 8.2 --- Different ways of implementation of BRIN for transitive closure --- p.61Chapter 8.2.1 --- Digital Implementation --- p.61Chapter 8.2.2 --- Analog Implementation --- p.61Chapter 8.3 --- Transitive Closure Problem --- p.63Chapter 8.3.1 --- A special case of maximum spanning tree problem --- p.64Chapter 8.3.2 --- Analog approach solution for transitive closure problem --- p.65Chapter 8.3.3 --- Current-mode approach solution for transitive closure problem --- p.67Chapter 8.4 --- Comparisons between the different forms of implementation of BRIN for transitive closure --- p.71Chapter 8.4.1 --- Convergence Time --- p.71Chapter 8.4.2 --- Circuit complexity --- p.72Chapter 8.5 --- Discussion --- p.73Chapter 9 --- Critical path problems --- p.74Chapter 9.1 --- Introduction --- p.74Chapter 9.2 --- Problem statement and single-destination BRIN solution --- p.75Chapter 9.3 --- Analog implementation --- p.76Chapter 9.3.1 --- Separated building block --- p.78Chapter 9.3.2 --- Combined building block --- p.79Chapter 9.4 --- Current-mode approach --- p.80Chapter 9.4.1 --- "Site function, unit output function and a completed network" --- p.80Chapter 9.5 --- Conclusion --- p.83Chapter 10 --- Conclusions --- p.85Chapter 10.1 --- Summary of Achievements --- p.85Chapter 10.2 --- Future development --- p.88Chapter 10.2.1 --- Application for financial problems --- p.88Chapter 10.2.2 --- Fabrication of VLSI Implementation --- p.88Chapter 10.2.3 --- Actual prototyping of Analog Integrated Circuits for critical path and transitive closure problems --- p.89Chapter 10.2.4 --- Other implementation platform --- p.89Chapter 10.2.5 --- On-line update of routing table inside the router for network com- munication using BRIN --- p.89Chapter 10.2.6 --- Other BRIN's applications --- p.90Bibliography --- p.9

Effective network grid synthesis and optimization for high performance very large scale integration system design

制度:新 ; 文部省報告番号:甲2642号 ; 学位の種類:博士(工学) ; 授与年月日:2008/3/15 ; 早大学位記番号:新480

Applications and implementation of neuro-connectionist architectures.

by H.S. Ng.Thesis (M.Phil.)--Chinese University of Hong Kong, 1996.Includes bibliographical references (leaves 91-97).Chapter 1 --- Introduction --- p.1Chapter 1.1 --- Introduction --- p.1Chapter 1.2 --- Neuro-connectionist Network --- p.2Chapter 2 --- Related Works --- p.5Chapter 2.1 --- Introduction --- p.5Chapter 2.1.1 --- Kruskal's Algorithm --- p.5Chapter 2.1.2 --- Prim's algorithm --- p.6Chapter 2.1.3 --- Sollin's algorithm --- p.7Chapter 2.1.4 --- Bellman-Ford algorithm --- p.8Chapter 2.1.5 --- Floyd-Warshall algorithm --- p.9Chapter 3 --- Binary Relation Inference Network and Path Problems --- p.11Chapter 3.1 --- Introduction --- p.11Chapter 3.2 --- Topology --- p.12Chapter 3.3 --- Network structure --- p.13Chapter 3.3.1 --- Single-destination BRIN architecture --- p.14Chapter 3.3.2 --- Comparison between all-pair BRIN and single-destination BRIN --- p.18Chapter 3.4 --- Path Problems and BRIN Solution --- p.18Chapter 3.4.1 --- Minimax path problems --- p.18Chapter 3.4.2 --- BRIN solution --- p.19Chapter 4 --- Analog and Voltage-mode Approach --- p.22Chapter 4.1 --- Introduction --- p.22Chapter 4.2 --- Analog implementation --- p.24Chapter 4.3 --- Voltage-mode approach --- p.26Chapter 4.3.1 --- The site function --- p.26Chapter 4.3.2 --- The unit function --- p.28Chapter 4.3.3 --- The computational unit --- p.28Chapter 4.4 --- Conclusion --- p.29Chapter 5 --- Current-mode Approach --- p.32Chapter 5.1 --- Introduction --- p.32Chapter 5.2 --- Current-mode approach for analog VLSI Implementation --- p.33Chapter 5.2.1 --- Site and Unit output function --- p.33Chapter 5.2.2 --- Computational unit --- p.34Chapter 5.2.3 --- A complete network --- p.35Chapter 5.3 --- Conclusion --- p.37Chapter 6 --- Neural Network Compensation for Optimization Circuit --- p.40Chapter 6.1 --- Introduction --- p.40Chapter 6.2 --- A Neuro-connectionist Architecture for error correction --- p.41Chapter 6.2.1 --- Linear Relationship --- p.42Chapter 6.2.2 --- Output Deviation of Computational Unit --- p.44Chapter 6.3 --- Experimental Results --- p.46Chapter 6.3.1 --- Training Phase --- p.46Chapter 6.3.2 --- Generalization Phase --- p.48Chapter 6.4 --- Conclusion --- p.50Chapter 7 --- Precision-limited Analog Neural Network Compensation --- p.51Chapter 7.1 --- Introduction --- p.51Chapter 7.2 --- Analog Neural Network hardware --- p.53Chapter 7.3 --- Integration of analog neural network compensation of connectionist net- work for general path problems --- p.54Chapter 7.4 --- Experimental Results --- p.55Chapter 7.4.1 --- Convergence time --- p.56Chapter 7.4.2 --- The accuracy of the system --- p.57Chapter 7.5 --- Conclusion --- p.58Chapter 8 --- Transitive Closure Problems --- p.60Chapter 8.1 --- Introduction --- p.60Chapter 8.2 --- Different ways of implementation of BRIN for transitive closure --- p.61Chapter 8.2.1 --- Digital Implementation --- p.61Chapter 8.2.2 --- Analog Implementation --- p.61Chapter 8.3 --- Transitive Closure Problem --- p.63Chapter 8.3.1 --- A special case of maximum spanning tree problem --- p.64Chapter 8.3.2 --- Analog approach solution for transitive closure problem --- p.65Chapter 8.3.3 --- Current-mode approach solution for transitive closure problem --- p.67Chapter 8.4 --- Comparisons between the different forms of implementation of BRIN for transitive closure --- p.71Chapter 8.4.1 --- Convergence Time --- p.71Chapter 8.4.2 --- Circuit complexity --- p.72Chapter 8.5 --- Discussion --- p.73Chapter 9 --- Critical path problems --- p.74Chapter 9.1 --- Introduction --- p.74Chapter 9.2 --- Problem statement and single-destination BRIN solution --- p.75Chapter 9.3 --- Analog implementation --- p.76Chapter 9.3.1 --- Separated building block --- p.78Chapter 9.3.2 --- Combined building block --- p.79Chapter 9.4 --- Current-mode approach --- p.80Chapter 9.4.1 --- "Site function, unit output function and a completed network" --- p.80Chapter 9.5 --- Conclusion --- p.83Chapter 10 --- Conclusions --- p.85Chapter 10.1 --- Summary of Achievements --- p.85Chapter 10.2 --- Future development --- p.88Chapter 10.2.1 --- Application for financial problems --- p.88Chapter 10.2.2 --- Fabrication of VLSI Implementation --- p.88Chapter 10.2.3 --- Actual prototyping of Analog Integrated Circuits for critical path and transitive closure problems --- p.89Chapter 10.2.4 --- Other implementation platform --- p.89Chapter 10.2.5 --- On-line update of routing table inside the router for network com- munication using BRIN --- p.89Chapter 10.2.6 --- Other BRIN's applications --- p.90Bibliography --- p.9