BDD-Based Boolean Functional Synthesis

  • Dror Fried
  • Lucas M. TabajaraEmail author
  • Moshe Y. Vardi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9780)


Boolean functional synthesis is the process of automatically obtaining a constructive formalization from a declarative relation that is given as a Boolean formula. Recently, a framework was proposed for Boolean functional synthesis that is based on Craig Interpolation and in which Boolean functions are represented as And-Inverter Graphs (AIGs). In this work we adapt this framework to the setting of Binary Decision Diagrams (BDDs), a standard data structure for representation of Boolean functions. Our motivation in studying BDDs is their common usage in temporal synthesis, a fundamental technique for constructing control software/hardware from temporal specifications, in which Boolean synthesis is a basic step. Rather than using Craig Interpolation, our method relies on a technique called Self-Substitution, which can be easily implemented by using existing BDD operations. We also show that this yields a novel way to perform quantifier elimination for BDDs. In addition, we look at certain BDD structures called input-first, and propose a technique called TrimSubstitute, tailored specifically for such structures. Experiments on scalable benchmarks show that both Self-Substitution and TrimSubstitute scale well for benchmarks with good variable orders and significantly outperform current Boolean-synthesis techniques.


Boolean Function Terminal Node Boolean Formula Binary Decision Diagram Quantifier Elimination 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



This work is supported in part by NSF grants CCF-1319459 and IIS-1527668, by NSF Expeditions in Computing project “ExCAPE: Expeditions in Computer Augmented Program Engineering”, by BSF grant 9800096, and by the Brazilian agencies CAPES and CNPq through the Ciência Sem Fronteiras program


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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Dror Fried
    • 1
  • Lucas M. Tabajara
    • 1
    Email author
  • Moshe Y. Vardi
    • 1
  1. 1.Department of Computer ScienceRice UniversityHoustonUSA

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