Exact Synthesis of ESOP Forms

  • Heinz RienerEmail author
  • Rüdiger Ehlers
  • Bruno de O. Schmitt
  • Giovanni De Micheli


We present an exact synthesis approach for computing Exclusive-or Sum-of-Products (ESOP) forms with a minimum number of product terms using Boolean satisfiability. Our approach finds one or more ESOP forms for a given Boolean function. The approach can deal with incompletely specified Boolean functions defined over many Boolean variables and is particularly fast if the Boolean function can be expressed with only a few product terms. We describe the formalization of the ESOP synthesis problem with a fixed number of terms as a decision problem and present search procedures for determining ESOP forms of minimum size. We further discuss how the search procedures can be relaxed to find ESOP forms of small sizes in reasonable time. We experimentally evaluate the performance of the SAT-based synthesis procedures on completely and incompletely specified Boolean functions.


Logic synthesis ESOP Exact synthesis Logic minimization Reed–Muller forms 



This research was supported by H2020-ERC-2014-ADG 669354 CyberCare (200021-146600) and the Institutional Strategy of the University of Bremen, funded by the German Excellence Initiative.


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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Heinz Riener
    • 1
    Email author
  • Rüdiger Ehlers
    • 2
  • Bruno de O. Schmitt
    • 1
  • Giovanni De Micheli
    • 1
  1. 1.EPFLLausanneSwitzerland
  2. 2.University of BremenBremenGermany

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