Chakraborty, SupratikMeel, Kuldeep S.Vardi, Moshe Y.2017-08-022017-08-022016-11-28Chakraborty, Supratik, Meel, Kuldeep S. and Vardi, Moshe Y.. "Algorithmic Improvements in Approximate Counting for Probabilistic Inference: From Linear to Logarithmic SAT Calls*." (2016) https://hdl.handle.net/1911/96419.https://hdl.handle.net/1911/96419Probabilistic inference via model counting has emerged as a scalable technique with strong formal guarantees, thanks to recent advances in hashing-based approximate counting. State-of-the-art hashing-based counting algorithms use an NP oracle (SAT solver in practice), such that the number of oracle invocations grows linearly in the number of variables n in the input constraint. We present a new approach to hashing-based approximate model counting in which the number of oracle invocations grows logarithmically in n, while still providing strong theoretical guarantees. We use this technique to design an algorithm for #CNF with probably approximately correct (PAC) guarantees. Our experiments show that this algorithm outperforms state-of-the-art techniques for approximate counting by 1-2 orders of magnitude in running time. We also show that our algorithm can be easily adapted to give a new fully polynomial randomized approximation scheme (FPRAS) for #DNF14 ppengYou are granted permission for the noncommercial reproduction, distribution, display, and performance of this technical report in any format, but this permission is only for a period of forty-five (45) days from the most recent time that you verified that this technical report is still available from the Computer Science Department of Rice University under terms that include this permission. All other rights are reserved by the author(s).Technical reportTR16-03