Open Problems

  • Srimat T. Chakradhar
  • Vishwani D. Agrawal
  • Michael L. Bushneil
Part of the The Springer International Series in Engineering and Computer Science book series (SECS, volume 140)


The research reported in the proceeding chapters opens up a new line of thought relating test generation to general optimization problems. We hope the reader will be tempted to find solutions to other currently open problems including the ones listed below:
  • Parallelization of the graph-theoretic test generation technique. Recall (see Chapter 9) that in this technique, we split the energy function into two sub-functions. A solution to one sub-function, the homogeneous posiform, is obtained very quickly and we check to see if this solution satisfies the other sub-function. One way to parallelize this technique would be to generate several solutions of the homogeneous posiform in parallel and check these, again in parallel, against the other sub-function. This method holds promise since the solution-generating method as well as the solution-checking phase can easily be parallelized.

  • Enhancement of the basic test generation formulation. We have presented several enhancements (see Chapters 8,9 and 10) to the basic formulation and we believe more test generation knowledge can be incorporated into the energy function.

  • Simulation of the neural network on parallel or pipelined computers. Since neurons can be synchronous and use only local information to update their state, the Connection Machine [3] architecture seems to be most suitable for neural network simulations. Similarly, a pipelined machine like MARS [1], which provides fast logic simulation, can be programmed for this application.

  • Identification of a good initial state of the neural network. We have empirically observed that the center of the hypercube representing the search space is a good initial state. Further research should lead to a better insight into the selection of good starting points for the gradient descent search and the analog neural network.

  • Extension to sequential circuits. The work reported here deals with combinational circuits. Recently, Fujiwara [2] has extended ourneural models to handle three logic values (0, 1 and X). Extending this work to sequential circuits requires neural models of three-state logic. More work is, however, needed to account for the extra degree of freedom (time) in sequential circuits.

  • Development of a good design-for-testability technique. We have identified a new, easily-testable class of circuits, namely the (k, K)circuits (see Chapter 11). Design of (k, K)-circuits is an open problem in the area of synthesis for testability.

  • Isolation of new, easily solvable instances of NP-complete problems. We have isolated special instances that map into combinational circuits. This is a new method of solving such problems. In Chapter 13 we apply it to solve the maximum weighted independent set problem. We believe that using similar techniques, a much larger class of easily-solvable instances can be identified. Some of these instances may map onto sequential circuits.


Test Generation Sequential Circuit Combinational Circuit Logic Simulation Neural Network Simulation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. [1]
    P. Agrawal and WJ. Dally. A Hardware Logic Simulation System. IEEE Transactions on Computer-Aided Design, CAD-9(1): 19–29, January 1990.CrossRefGoogle Scholar
  2. [2]
    H. Fujiwara. Three-valued Neural Networks for Test Generation. In Proceedings of the 20th IEEE International Symposium on Fault Tolerant Computing, pages 64–71, June 1990.Google Scholar
  3. [3]
    W. D. Hillis. The Connection Machine. The MIT Press, Cambridge, Massachusetts, 1985.Google Scholar

Copyright information

© Springer Science+Business Media New York 1991

Authors and Affiliations

  • Srimat T. Chakradhar
    • 1
  • Vishwani D. Agrawal
    • 2
  • Michael L. Bushneil
    • 3
  1. 1.NEC Research InstituteUSA
  2. 2.AT&T Bell LaboratoriesUSA
  3. 3.Rutgers UniversityUSA

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