The Connectivity of Boolean Satisfiability: Computational and Structural Dichotomies

  title={The Connectivity of Boolean Satisfiability: Computational and Structural Dichotomies},
  author={Parikshit Gopalan and Phokion G. Kolaitis and Elitza N. Maneva and Christos H. Papadimitriou},
  journal={Electron. Colloquium Comput. Complex.},
Given a Boolean formula, do its solutions form a connected subgraph of the hypercube? This and other related connectivity considerations underlie recent work on random Boolean satisfiability. We study connectivity properties of the space of solutions of Boolean formulas, and establish computational and structural dichotomies. Specifically, we first establish a dichotomy theorem for the complexity of the st-connectivity problem for Boolean formulas in Schaefer's framework. Our result asserts… 

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