# System theoretic models for high-density VLSI (very large scale integration) structures. Final technical report

## Abstract

This research project involved the development of mathematical models for analysis, synthesis, and simulation of large systems of interacting devices. The work was motivated by problems that may become important in high-density VLSI chips with characteristic feature sizes less than 1 micron: it is anticipated that interactions of neighboring devices will play an important role in the determination of circuit properties. It is hoped that the combination of high device densities and such local interactions can somehow be exploited to increase circuit speed and to reduce power consumption. To address these issues from the point of view of system theory, research was pursued in the areas of nonlinear and stochastic systems and into neural-network models. Statistical models were developed to characterize various features of the dynamic behavior of interacting systems. Random-process models for studying the resulting asynchronous modes of operation were investigated. The local interactions themselves may be modeled as stochastic effects. The resulting behavior was investigated through the use of various scaling limits, and by a combination of other analytical and simulation techniques. Techniques arising in a variety of disciplines where models of interaction have been formulated and explored were considered and adapted for use.

- Authors:

- Publication Date:

- Research Org.:
- Princeton Univ., NJ (USA). Dept. of Electrical Engineering and Computer Science

- OSTI Identifier:
- 5549382

- Alternate Identifier(s):
- OSTI ID: 5549382

- Report Number(s):
- AD-A-209901/8/XAB

- Resource Type:
- Technical Report

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; 42 ENGINEERING; INTEGRATED CIRCUITS; SYSTEMS ANALYSIS; ENERGY CONSUMPTION; MATHEMATICAL MODELS; OPERATION; PROGRESS REPORT; SIMULATION; STOCHASTIC PROCESSES; VELOCITY; DOCUMENT TYPES; ELECTRONIC CIRCUITS; MICROELECTRONIC CIRCUITS 990210* -- Supercomputers-- (1987-1989); 420800 -- Engineering-- Electronic Circuits & Devices-- (-1989)

### Citation Formats

```
Dickinson, B.W., and Hopkins, W.E.
```*System theoretic models for high-density VLSI (very large scale integration) structures. Final technical report*. United States: N. p., 1989.
Web.

```
Dickinson, B.W., & Hopkins, W.E.
```*System theoretic models for high-density VLSI (very large scale integration) structures. Final technical report*. United States.

```
Dickinson, B.W., and Hopkins, W.E. Sun .
"System theoretic models for high-density VLSI (very large scale integration) structures. Final technical report". United States.
doi:.
```

```
@article{osti_5549382,
```

title = {System theoretic models for high-density VLSI (very large scale integration) structures. Final technical report},

author = {Dickinson, B.W. and Hopkins, W.E.},

abstractNote = {This research project involved the development of mathematical models for analysis, synthesis, and simulation of large systems of interacting devices. The work was motivated by problems that may become important in high-density VLSI chips with characteristic feature sizes less than 1 micron: it is anticipated that interactions of neighboring devices will play an important role in the determination of circuit properties. It is hoped that the combination of high device densities and such local interactions can somehow be exploited to increase circuit speed and to reduce power consumption. To address these issues from the point of view of system theory, research was pursued in the areas of nonlinear and stochastic systems and into neural-network models. Statistical models were developed to characterize various features of the dynamic behavior of interacting systems. Random-process models for studying the resulting asynchronous modes of operation were investigated. The local interactions themselves may be modeled as stochastic effects. The resulting behavior was investigated through the use of various scaling limits, and by a combination of other analytical and simulation techniques. Techniques arising in a variety of disciplines where models of interaction have been formulated and explored were considered and adapted for use.},

doi = {},

journal = {},

number = ,

volume = ,

place = {United States},

year = {Sun Jan 01 00:00:00 EST 1989},

month = {Sun Jan 01 00:00:00 EST 1989}

}