"Empty space" computes: the evolution of an unconventional supercomputer

ABSTRACT

Lee A. Rubel defined the extended analog computer to avoid the limitations of Shannon's general purpose analog computer. Partial differential equation solvers were a "quintessential" part of Rubel's theoretical machine. These components have been implemented with "empty space," or VLSI circuits without transistors, as well as conductive plastic. For the past decade research at Indiana University has explored the design and applications of extended analog computers. The machines have become increasingly sophisticated and flexible. The "empty" computational area is devoted to solving partial differential equations. The rest of the space includes fuzzy logic elements, configuration memory and input/output channels. This paper describes the theoretical definition, architecture and implementation of these unconventional computers. Two parallel applications are described in detail. Rubel's model can be viewed as an abstract specification for a distributed supercomputer. We close with a description of an inexpensive 64-node processor that was designed using our current single processor. The next step is to return to VLSI with an improved understanding of the architecture-and seek computation speeds approaching trillions of partial differential equations per second.

REFERENCES

• 1: Ainslie, N. et. al. Toward the Evolution of Analog Computers for Control of Data Networks. B644 VLSI Design. Indiana University, 2002.
• 2: Biswas, A. Some Investigations with Laser Beams on an LLA Retina, MS Thesis, Indiana University Computer Science Department, 1994.
• 3: Blair, H. Verification of Hybrid Systems. 1 st Workshop Computation on the Continuum. Lisbon, Portugal. 2005.
• 4: Conrad, J. Stiquito Controlled! John Wiley: NY, 2005
• 5: Girvin, S. Private communication. 1994.
• 6: Graca, D. Computability in the GPAC. 1 st Workshop Computation on the Continuum. Lisbon, Portugal. 2005.
• 7: Himebaugh, B. Design of a Flexible EAC. 2006.
• 8: Lee W. Hoevel , Michael J. Flynn, The structure of directly executed languages: a new theory of interpretive system design, Stanford University, Stanford, CA, 1977
• 9: Karplus, W. Analog Simulation. McGraw-Hill: NY, 1958.
• 10: Maass, W. and E. Sontag. Analog Neural Nets with Gaussian or other Common Noise Distributions Cannot Recognize Arbitrary Regular Languages. (no date).
• 11: McNaughton, R. A theorem about infinite-valued sentential logic. J. Symbolic Logic, 16 1--13, 1950.
• 12: Carver Mead, Analog VLSI and neural systems, Addison-Wesley Longman Publishing Co., Inc., Boston, MA, 1989
• 13: Mills, J., N. Miller and J. Nakamura. The Jell-O ® Brand Gelatin Processor: A Prototype Colloidal Computer. B644 VLSI Design. Indiana University, 2004.
• 14: Mills, J. The Continuous Retina: Image Processing with a Single-Sensor Artificial Neural Field Network. Proc. IEEE Conf. Neural Network, 1996.
• 15: Mills, J. Using the EAC for Traffic Management. 2000.
• 16: Nijhout, F. Development and Evolution of Butterfly Wing Patterns. Smithsonian Inst. Press: Wash., D.C., 1991.
• 17: Olowoweye, B. "Image Rendering Using Wave Theory of Light and Extended Analog Computers, Indiana University Computer Science Department Technical Report 581, 2003.
• 18: Pour-El, M. B. Abstract computability and its relation to the general-purpose analog computer. Trans. Amer. Math. Soc., 199 1--28, 1974.
• 19: Lee A. Rubel, The extended analog computer, Advances in Applied Mathematics, v.14 n.1, p.39-50, March 1993 [doi>10.1006/aama.1993.1003 ]
• 20: Rubel, L. The Brain as an Analog Computer. J. Theor. Neurobiol. 4. 000--000. 1985.
• 21: Rubel, L. Private communication. 1994.
• 22: Sandved, K. The Butterfly Alphabet Poster. 2000.
• 23: Shannon, C. Mathematical Theory of the Differential Analyzer. J. Math. And Physics 20 337--354, 1941.
• 24: Hava T. Siegelmann , Eduardo D. Sontag, On the computational power of neural nets, Proceedings of the fifth annual workshop on Computational learning theory, p.440-449, July 27-29, 1992, Pittsburgh, Pennsylvania, United States [doi>10.1145/130385.130432]
• 25: Williams, B. D. Kipfer, J. Mails and J. Hartzell. A Virtual Light Interface for the Extended Analog Computer. B644 VLSI Design. Indiana University, 2005

INDEX TERMS

Primary Classification:
  C. Computer Systems Organization
  C.1 PROCESSOR ARCHITECTURES
      C.1.3 Other Architecture Styles

Additional Classification:
  B. Hardware
  B.7 INTEGRATED CIRCUITS
      B.7.1 Types and Design Styles
          Subjects: VLSI (very large scale integration); Advanced technologies

  C. Computer Systems Organization
  C.5 COMPUTER SYSTEM IMPLEMENTATION
      C.5.1 Large and Medium ("Mainframe") Computers
          Subjects: Super (very large) computers

  F. Theory of Computation
  F.1 COMPUTATION BY ABSTRACT DEVICES
      F.1.2 Modes of Computation
          Subjects: Probabilistic computation; Parallelism and concurrency

  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.8 Partial Differential Equations
          Subjects: Multigrid and multilevel methods

General Terms:
Design, Experimentation

Keywords:
Lukasiewicz logic, extended analog computer, general purpose analog computer, hybrid digital-analog architecture