Random 3-SAT and BDDs: The Plot Thickens Further

  • Alfonso San Miguel Aguirre
  • MosheY. Vardi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2239)


This paper contains an experimental study of the impact of the construction strategy of reduced, ordered binary decision diagrams (ROBDDs) on the average-case computational complexity of random 3-SAT, using the CUDD package.We study the variation of median running times for a large collection of random 3-SAT problems as a function of the density as well as the order (number of variables) of the instances.We used ROBDD-based pure SAT-solving algorithms, which we obtained by an aggressive application of existential quantification, augmented by several heuristic optimizations. Our main finding is that our algorithms display an “easy-hard-less-hard” pattern that is quite similar to that observed earlier for search-based solvers. When we start with low-density instances and then increase the density, we go from a region of polynomial running time, to a region of exponential running time, where the exponent first increases and then decreases as a function of the density. The locations of both transitions, from polynomial to exponential and from increasing to decreasing exponent, are algorithm dependent. In particular, the running time peak is quite independent from the crossover density of 4.26 (where the probability of satisfiability declines precipitously); it occurs at density 3.8 for one algorithm and at density 2.3 for for another, demonstrating that the correlation between the crossover density and computational hardness is algorithm dependent.


Boolean Function Binary Decision Diagram Symbolic Model Check Input Formula Ordered Binary Decision Diagram 
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.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Alfonso San Miguel Aguirre
    • 1
  • MosheY. Vardi
    • 2
  1. 1.Dept. of Computer ScienceInstituto Tecnologico Autonomo de MexicoMexico CityMexico
  2. 2.Department of Computer ScienceRice UniversityHoustonUSA

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