Transformations of Boolean Functions

Authors Jeffrey M. Dudek , Dror Fried

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Jeffrey M. Dudek
  • Department of Computer Science, Rice University, Houston, TX, USA
Dror Fried
  • Department of Mathematics and Computer Science, The Open University of Israel, Ra’anana, Israel


We would like to thank Kuldeep S. Meel, Moshe Y. Vardi, and Rice’s Computer-Aided Verification Group for useful discussions.

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Jeffrey M. Dudek and Dror Fried. Transformations of Boolean Functions. In 39th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 150, pp. 39:1-39:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


Boolean functions are characterized by the unique structure of their solution space. Some properties of the solution space, such as the possible existence of a solution, are well sought after but difficult to obtain. To better reason about such properties, we define transformations as functions that change one Boolean function to another while maintaining some properties of the solution space. We explore transformations of Boolean functions, compactly described as Boolean formulas, where the property is to maintain is the number of solutions in the solution spaces. We first discuss general characteristics of such transformations. Next, we reason about the computational complexity of transforming one Boolean formula to another. Finally, we demonstrate the versatility of transformations by extensively discussing transformations of Boolean formulas to "blocks," which are solution spaces in which the set of solutions makes a prefix of the solution space under a lexicographic order of the variables.

Subject Classification

ACM Subject Classification
  • Theory of computation → Logic and verification
  • Boolean Formulas
  • Boolean Functions
  • Transformations
  • Model Counting


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