Decomposing a System of Boolean Functions into Subsystems of Connected Functions

  • P. N. BibiloEmail author


This paper suggests some algorithms for decomposing a system of Boolean functions into subsystems of connected functions for representations such as truth tables (TTs), systems of disjunctive normal forms (DNFs), and binary decision diagrams (BDDs). The connectivity of functions consists of the presence of identical parts in the domains of functions from a given system. The algorithms are heuristic and can be used in computer-aided synthesis systems for real-dimension problems with several hundred functions, each having several tens of arguments. The experiments described below prove the efficiency of this decomposition approach in the logic optimization of a system of Boolean functions based on Shannon’s decomposition with the possible use of subfunction inversions.



  1. 1.
    K. R. Brayton, G. D. Hactel, and A. L. Sangiovanni-Vincentelli, “Synthesis of multi-level combinational logic circuits,” TIIER 78 (2) (1990).Google Scholar
  2. 2.
    K. R. Brayton, G. D. Hactel, C. T. McMullen, and A. L. Sangiovanni-Vincentelli, Logic Minimization Algorithm for VLSI Synthesis (Kluwer Academic, Dordrecht, 1984).CrossRefzbMATHGoogle Scholar
  3. 3.
    A. D. Zakrevskii, Yu. V. Pottosin, and L. D. Cheremisinova, The Logical Basis of the Designing the Discrete Tools (Fizmatlit, Moscow, 2007) [in Russian].Google Scholar
  4. 4.
    P. N. Bibilo, Application of Binary Choice Diagrams in the Synthesis of Logic Circuits (Belarus. Navuka, Minsk, 2014) [in Russian].Google Scholar
  5. 5.
    M. A. Gavrilov, “Composition and decomposition of combinational automata,” in Automata Theory (Nauka, Moscow, 1976) [in Russian].Google Scholar
  6. 6.
    M. A. Gavrilov, V. V. Devyatkov, and E. I. Pupyrev, Logical Design of Discrete Automata (Nauka, Moscow, 1977) [in Russian].Google Scholar
  7. 7.
    O. P. Kuznetsov, “On software implementation of logic functions and automata,” Avtom. Telemekh., No. 7 (1977).Google Scholar
  8. 8.
    R. E. Bryant and C. Meinel, “Ordered binary decision diagrams,” in Logic Synthesis and Verification, Ed. by S. Hassoun, T. Sasao, and R. K. Brayton (Kluwer Academic, Dordrecht, 2002).Google Scholar
  9. 9.
    S. Yang and M. Ciesielski, “BDS: a BDD-based logic optimization system,” IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst. 21 (7) (2002).Google Scholar
  10. 10.
    P. N. Bibilo, Decomposition of Boolean Functions Based on the Solution of Logical Equations (Belarus. Navuka, Minsk, 2009) [in Russian].Google Scholar
  11. 11.
    P. N. Bibilo, N. A. Kirienko, and Yu. Yu. Lankevich, “Logical optimization the multilevel representations of systems of Boolean functions based on partitioning into blocks and Shannon decomposition,” Informatika 15 (3), 56–70 (2018).Google Scholar
  12. 12.
    Yu. V. Pottosin and E. A. Shestakov, “Orthogonalization of a system of fully defined boolean functions,” in Logical Design, Collection of Articles (Inst. Tekh. Kibern. NAN Belarusi, Minsk, 2000), No. 5 [in Russian].Google Scholar
  13. 13.
    A. D. Zakrevskii, Calculations in Multidimensional Boolean Space (OIPI NAN Belarusi, Minsk, 2011) [in Russian].Google Scholar
  14. 14.
    P. N. Bibilo, Synthesis of Combination PLA-Structures for VLSI (Nauka Tekh., Minsk, 1992) [in Russian].Google Scholar
  15. 15.
    D. E. Knuth, The Art of Computer Programming (Addison-Wesley, Reading, MA, 2011), Vol. 4.zbMATHGoogle Scholar
  16. 16.
    P. N. Bibilo and V. I. Romanov, Logical Design of Discrete Devices Using Production-Frame Model of Knowledge Representation (Belarus. Navuka, Minsk, 2011) [in Russian].Google Scholar
  17. 17.
    P. N. Bibilo and Yu. Yu. Lankevich, “The use of Zhegalkin polynomials for minimization of multilevel representations of Boolean functions based on Shannon expansion,” Program. Inzhen. 8, 369–384 (2017).Google Scholar
  18. 18.
    C. Jeong, Computer-Aided Design of Digital Systems, Department of Computer Science. Scholar
  19. 19.
    P. N. Bibilo and N. A. Avdeev, VHDL. Effective Use in the Design of Digital Systems (SOLON-Press, Moscow, 2006) [in Russian].Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.United Institute of Informatics Problems, National Academy of Sciences of BelarusMinskBelarus

Personalised recommendations