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Minimal covering problem and PLA minimization

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Abstract

Solving the minimal covering problem by an implicit enumeration method is discussed. The implicit enumeration method in this paper is a modification of the Quine-McCluskey method tailored to computer processing and also its extension, utilizing some new properties of the minimal covering problem for speedup. A heuristic algorithm is also presented to solve large-scale problems. Its application to the minimization of programmable logic arrays (i.e., PLAs) is shown as an example. Computational experiences are presented to confirm the improvements by the implicit enumeration method discussed.

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References

  1. E. J. McCluskey,Introduction to the Theory of Switching Circuits, McGraw-Hill (1965).

  2. M.-H. Young, The Minimal Covering Problem and Automated Design of Two-level AND/OR Optimal Networks, Ph.D. Dissertation, Report No. UIUCDCS-R-79-966, Department Computer Science, University of Illinois, Urbana, 186 pp. (1979).

    Google Scholar 

  3. S. Muroga,Logic Design and Switching Theory, John Wiley & Sons, New York (1979).

    Google Scholar 

  4. S. Muroga,VLSI System Design, John Wiley & Sons, New York (1982).

    Google Scholar 

  5. E. Balas, An Additive Algorithm for Solving Linear Programs with 0–1 Variables,Operations Research 13:517–546 (1965).

    Google Scholar 

  6. A. Cobham, R. Fridshal, and J. H. North, An Application of Linear Programming to the Minimization of Boolean Functions,Proc. Second Ann. Symp. Switching Circuit Theory and Logic Design, pp. 3–9 (1961).

  7. T. Ibaraki, T. K. Liu, C. R. Baugh, and S. Muroga, An Implicit Enumeration Program for Zero-One Integer Programming,Int. J. of Comput. and Info. Sci. 1(1):75–92 (March 1972).

    Google Scholar 

  8. J. Haldi, 25 Integer Programming Test Problems, Working Paper No. 43, Graduate School of Business, Stanford University (December 1964).

  9. A. M. Geoffrion, An Improved Implicit Enumeration Approach to Integer Programming,Operations Research 17:437–454 (1969).

    Google Scholar 

  10. J. F. Shapiro, Group Theoretical Algorithms for the Integer Programming Problem-II: Extension to a General Algorithm,Oper. Res. 16:928–947 (1968).

    Google Scholar 

  11. C. A. Trauth and R. E. Woolsey, Integer Linear Programming: A Study in Computational Efficiency,Man. Sci. 15:481–493 (1969).

    Google Scholar 

  12. L. E. Trotter, Jr., and C. M. Shetty, An Algorithm for the Bounded Variable Integer Programming Problem,J. ACM 21(3):505–513 (July 1974).

    Google Scholar 

  13. D. R. Fulkerson, G. L. Nemhauser, and L.E. Trotter, Jr., Two Computationally Difficult Set Covering Problems That Arise in Computing the 1-Width of Steiner Triple Systems, Mathematical Programming Study 2, North-Holland Publishing Company, pp. 72–81 (1974).

  14. Computer Characteristic Quarterly, Adams Associates, Inc. (1968).

  15. Standard EDP Report, Auerbach Info., Inc. (1972).

  16. A. Cobham, R. Fridshal, and J. H. North, A Statistical Study of the Minimization of Boolean Functions Using Integer Programming, IBM Research Report, RC-756 (1962).

  17. R. M. Bowman and E. S. McVey, A Method for the Fast Approximate Solutions of Large Prime Implicant Charts,IEEE Trans. Comput. C-19:169–173 (February 1970).

    Google Scholar 

  18. R. Roth, Computer Solution to Minimum-covering Problems,Operations Research,17: 455–465 (1969).

    Google Scholar 

  19. M.-H. Young, “Program Manual of Programs for Minimal Covering Problems: ILLOD-MINIC-B, ILLOD-MINIC-BP, ILLOD-MINIC-BS, ILLOD-MINIC-BA, ILLOD-MINIC-BG,” Report No. UIUCDCS-R-78-924, Department of Computer Science, University of Illinois, Urbana (1978).

    Google Scholar 

  20. M.-H. Young and S. Muroga, Symmetric Minimal Covering Problem and Minimal PLAs with Symmetric Variables,IEEE Trans. Comput. C-34(6): 523–541 (June 1985).

    Google Scholar 

  21. M.-H. Young and R. B. Cutler, Program Manual for the Programs ILLOD-MINSUM-CBS, ILLOD-MINSUM-CBSA, ILLOD-MINSUM-CBG, ILLOD-MINSUM-CBGM, to Derive Minimal Sums or Irredundant Disjunctive Forms for Switching Functions, Report No. UIUCDCS-R-78-926, Department of Computer Science, University of Illinois, Urbana (1978).

    Google Scholar 

  22. H.-M. Xu, User Manual for MINSUM-C System, Report, Department of Computer Science, University of Illinois, Urbana (1983).

    Google Scholar 

  23. C. Lemke and K. Spielberg, Direct Search 0–1 and Mixed Integer Programming,Operations Research 15:892–914 (1967).

    Google Scholar 

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Authors and Affiliations

  1. Silicon Compiler Inc., 2045 Hamilton Ave., 95125, San Jose, California

    Ming Huei Young

  2. Department of Computer Science, University of Illinois, 61801, Urbana, Illinois

    Saburo Muroga

Authors
  1. Ming Huei Young
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  2. Saburo Muroga
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Additional information

This work was supported in part by the National Science Foundation under Grants Nos. MCS77-09744 and MCS81-08505 and also by the Department of Computer Science.

M.-H. Young was with the Department of Computer Science, University of Illinois, Urbana, Illinois.

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Young, M.H., Muroga, S. Minimal covering problem and PLA minimization. International Journal of Computer and Information Sciences 14, 337–364 (1985). https://doi.org/10.1007/BF00991179

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  • DOI: https://doi.org/10.1007/BF00991179

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