Your browser does not support JavaScript!
http://iet.metastore.ingenta.com
1887

Formulation for the computation of Boolean operations

Formulation for the computation of Boolean operations

For access to this article, please select a purchase option:

Buy article PDF
£12.50
(plus tax if applicable)
Buy Knowledge Pack
10 articles for £75.00
(plus taxes if applicable)

IET members benefit from discounts to all IET publications and free access to E&T Magazine. If you are an IET member, log in to your account and the discounts will automatically be applied.

Learn more about IET membership 

Recommend Title Publication to library

You must fill out fields marked with: *

Librarian details
Name:*
Email:*
Your details
Name:*
Email:*
Department:*
Why are you recommending this title?
Select reason:
 
 
 
 
 
IEE Proceedings - Computers and Digital Techniques — Recommend this title to your library

Thank you

Your recommendation has been sent to your librarian.

Boolean or switching equations are powerful mathematical tools for digital logic. Several problems in digital circuit design, such as automatic test pattern generation, could be efficiently solved if fast procedures for solving Boolean equations were available. Several methods for solving this class of equations have been developed, but their efficiency is a problem. A new formulation for the computation of Boolean operations based on cubic representation of Boolean functions, termed the cube set method, is presented. The solutions provided by this approach are given as a set of cubes satisfying the disjoint property. Some definitions and theorems are given to describe the method and experimental results are presented.

References

    1. 1)
      • Y. WANG , C. M . Solving Boolean equations using ROSOP forms. IEEE Trans. , 2 , 171 - 177
    2. 2)
      • MALIK, S., WANG, A., BRAYTON, R., SANGIOVANNI-VINCENTELLI, A.: `Logic verification using binary decision diagrams in logic synthesis environment', Design Automation Conference, 1988, p. 624–628.
    3. 3)
      • W. DEL PICCHIA . A numerical algorithm for the resolution for Boolean equations. IEEE Trans. , 983 - 986
    4. 4)
      • KOZLOWSKI, T., DAGLESS, E.L., SAUL, J.M.: `An enhanced algorithm for the minimization of exclusive-OR sum-of-products for incompletely specified functions', Proceedings of IEEE International Conference on Computer design (ICCD'95), 1995, p. 244–249.
    5. 5)
      • P.R. BHATTACHARJEE , S.K. BASU , J.C. PAUL . Translation of the problem of complete test set generation to pseudo-Boolean programming. IEEE Trans. , 7 , 864 - 867
    6. 6)
      • R.T. STANION , A.D. BHATTACHARY , C. SECHEN . An efficient method for generating exhaustive test sets. IEEE Trans. , 12 , 1516 - 1525
    7. 7)
      • R.K. BRAYTON , G.D. HACHTEL , C.T. M , A.L. SANGIOVANNI-VINCENTELLI . (1984) , Logic minimization algorithms for VLSI synthesis.
    8. 8)
      • S. RUDEANU . (1974) , Boolean functions and equations.
    9. 9)
      • B. KRISHNAMURTHY , J.G. TOLLIS . Improved techniques for estimating signal probabilities. IEEE Trans. , 7 , 1041 - 1045
    10. 10)
      • CHAI, L.: `ESOP circuit minimization based on the function ON-set', Master's Thesis, 2000.
    11. 11)
      • P. STEPHAN , R.K. BRAYTON , A.L. SANGIOVANNI-VINCENTELLI . Combinational test generation using satisfiability. IEEE Trans. , 9 , 1167 - 1176
    12. 12)
      • G. BOOLE . (1854) , An investigation of the laws of thought.
    13. 13)
      • R. JAIN . (1991) , The art of computer systems performance analysis.
    14. 14)
      • S. RUDEANU . An algebraic approach to Boolean equations. IEEE Trans. , 206 - 207
    15. 15)
      • RUDELL, R.: `Dynamic variable ordering for ordered binary decision diagrams', International Conference on Computer-aided-design, 1993, p. 42–47.
    16. 16)
      • I. WEGENER . The size of reduced OBDD's and optimal read-once branching programs for almost all Boolean functions. IEEE Trans. , 11 , 1262 - 1269
    17. 17)
      • S. SVOBODA . An algorithm for solving Boolean equations. IEEE Trans. , 557 - 559
    18. 18)
      • P. TRABADO , A. LLORIS-RUIZ , J. ORTEGA-LOPERA . Solution of switching equations based on a tabular algebra. IEEE Trans. , 5 , 591 - 596
    19. 19)
      • MERCER, M., KAPUR, R., ROSS, D.: `Functional approaches to generating orderings for efficient symbolic representation', 29th Design Automation Conference, 1992, p. 40–45.
    20. 20)
      • R. BRYANT . Graph-based algorithm for Boolean function manipulation. IEEE Trans. , 8 , 677 - 691
    21. 21)
      • S. UNGER . Some additions to `Solution of switching equations based on a tabular algebra. IEEE Trans. , 3 , 365 - 367
    22. 22)
      • BULTER, K.M., ROSS, D.E., KAPUR, R., MERCER, M.R.: `Heuristics to compute variable orderings for efficient manipulation of ordered binary decision diagrams', 28th Design Automation Conference, 1991, p. 417–420.
http://iet.metastore.ingenta.com/content/journals/10.1049/ip-cdt_20010706
Loading

Related content

content/journals/10.1049/ip-cdt_20010706
pub_keyword,iet_inspecKeyword,pub_concept
6
6
Loading
This is a required field
Please enter a valid email address