Fast parallel algorithms for finding all prime implicants for discrete functions

  • W. Oberschelp
Section VI: Complexity Of Boolean Functions
Part of the Lecture Notes in Computer Science book series (LNCS, volume 171)


We consider the problem of enumerating the prime implicants of a given discrete function as a basic task of circuit theory. First, we count PI's for random Boolean functions. Then we use the well known lattice differentiation as a tool for finding implicants. The concept of a peak admits to characterize prime implicants, at least those with no improper domains. The improper case can be reduced to a lower dimensional problem. Since the peak test is local, a parallel algorithm is available. The time and space complexity turns out to be low measured in the input size.


Boolean Function Discrete Function Input Size Circuit Theory Prime Implicants 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Davio, M., Deschamps, J.P. and Thayse, A., Discrete and switching functions. McGraw-Hill 1978Google Scholar
  2. Friedman, A.D. and Menon, P.R., Theory & design of switching circuits, Pitman 1975Google Scholar
  3. Garey, M.R. and Johnson, D.S., Computers and intractability, Freeman & Co. 1979Google Scholar
  4. Klar, R. Digitale Rechenautomaten (3. Aufl.), de Gruyter 1983Google Scholar
  5. McCluskey, E.J., Minimization of Boolean functions, Bell Syst. Tech. Journ. 35 (1956), 1417–1444Google Scholar
  6. Meo, A.R., On the synthesis of many-variable switching functions. In: Biorci, G. (ed.), Network and switching theory, Academic Press 1968Google Scholar
  7. Mileto, F. and Putzolu, G., Average values of quantities appearing in Boolean Function minimization, IEEE Trans. El. Comp. 13 (1964), 87–92Google Scholar
  8. Mileto, F. and Putzolu, G., Statistical complexity of algorithms for Boolean functions minimization, Journ. ACM 12 (1965), 364–375Google Scholar
  9. Oberschelp, W. and Remlinger, J., Schaltkreistheorie, Schriften zur Informatik und Angewandten Mathematik der RWTH Aachen, to appear 1984Google Scholar
  10. Quine, W.V., The problem of simplyfiying truth functions, Amer. Math. Monthly 59 (1952), 521–531Google Scholar
  11. Savage, J.E., The complexity of computing, Wiley 1976Google Scholar
  12. Spaniol, O., Arithmetik in Rechenanlagen, Teubner 1976Google Scholar
  13. Thayse, A., Boolean calculus of differences, Springer 1981 (Lecture notes in Comp. Science No. 101)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1984

Authors and Affiliations

  • W. Oberschelp
    • 1
  1. 1.Lehrstuhl für Angewandte Mathematik, insbesondere InformatikRWTH AachenAachenGermany

Personalised recommendations