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Simplification of Incompletely Specified Flow Tables with the Help of Prime Closed Sets

Published: 01 October 1969 Publication History

Abstract

In this short note, an attempt has been made to arrive at a general algorithm for minimizing the number of internal states in an incompletely specified flow table. The closure property of the compatibility classes which cover a given flow table leads us to the derivation of a particular class of closed sets defined as irredundant prime closed sets. It has been shown that these prime closed sets in sequential circuit synthesis play an analogous role to that of the prime implicants in combinational circuit synthesis. A method has been described for determining all the irredundant prime closed sets and finding the minimal row flow table by suitably choosing one or a collection of those sets.

References

[1]
M. C. Paull and S. H. Unger, "Minimizing the number of states in incompletely. specified sequential switching functions," IRE Trans. Electronic Computers, vol. EC-8, pp. 356-367, September 1959.
[2]
E. J. McCluskey, "Minimimum state sequential circuits for a restricted class of incompletely specified flow tables," Bell Sys. Tech. J., Vol. 41, pp. 1759-1768, December 1962.
[3]
A. Grasselli and F. Luccio, "A method for minimizing the number of Internal states in incompletely specified sequential networks" IEEE Trans. Electronic Computers, vol. EC-14 pp. 350-359 June 1965.

Cited By

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  • (2015)MeMinProceedings of the IEEE/ACM International Conference on Computer-Aided Design10.5555/2840819.2840833(94-101)Online publication date: 2-Nov-2015
  • (1991)Exact and heuristic algorithms for the minimization of incompletely specified state machinesProceedings of the conference on European design automation10.5555/951513.951554(184-191)Online publication date: 25-Feb-1991
  • (1980)A Method for Minimizing Incompletely Specified Sequential MachinesIEEE Transactions on Computers10.1109/TC.1980.167565529:8(732-736)Online publication date: 1-Aug-1980
  • Show More Cited By

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Published In

cover image IEEE Transactions on Computers
IEEE Transactions on Computers  Volume 18, Issue 10
October 1969
111 pages

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IEEE Computer Society

United States

Publication History

Published: 01 October 1969

Author Tags

  1. Class set
  2. closed set
  3. closure condition table
  4. compatibility class
  5. cover chart
  6. flow table
  7. implication table
  8. maximum compatibility class
  9. minimal cover
  10. prime closed set
  11. prime compatibility class
  12. redundant and irredundant prime closed sets
  13. states of a flow table.

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Cited By

View all
  • (2015)MeMinProceedings of the IEEE/ACM International Conference on Computer-Aided Design10.5555/2840819.2840833(94-101)Online publication date: 2-Nov-2015
  • (1991)Exact and heuristic algorithms for the minimization of incompletely specified state machinesProceedings of the conference on European design automation10.5555/951513.951554(184-191)Online publication date: 25-Feb-1991
  • (1980)A Method for Minimizing Incompletely Specified Sequential MachinesIEEE Transactions on Computers10.1109/TC.1980.167565529:8(732-736)Online publication date: 1-Aug-1980
  • (1975)Minimization of Incompletely Specified Sequential MachinesIEEE Transactions on Computers10.1109/T-C.1975.22413724:11(1089-1100)Online publication date: 1-Nov-1975
  • (1973)Fast State Minimization of Incompletely Specified Sequential MachinesIEEE Transactions on Computers10.1109/T-C.1973.22368722:2(215-217)Online publication date: 1-Feb-1973
  • (1973)On a New Approach for Finding All the Modified Cut-Sets in an Incompatibility GraphIEEE Transactions on Computers10.1109/T-C.1973.22368322:2(187-193)Online publication date: 1-Feb-1973
  • (1971)An Improved Method of Prime C-Class Derivation in the State Reduction of Sequential NetworksIEEE Transactions on Computers10.1109/T-C.1971.22322120:2(229-231)Online publication date: 1-Feb-1971

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