Abstract
We present a probabilistic model counter that can trade off running time with approximation accuracy. As in several previous works, the number of models of a formula is estimated by adding random parity constraints (equations). One key difference with prior works is that the systems of parity equations used correspond to the parity check matrices of Low Density Parity Check (LDPC) error-correcting codes. As a result, the equations tend to be much shorter, often containing fewer than 10 variables each, making the search for models that also satisfy the parity constraints far more tractable. The price paid for computational tractability is that the statistical properties of the basic estimator are not as good as when longer constraints are used. We show how one can deal with this issue and derive rigorous approximation guarantees by performing more solver invocations.
Research supported by NSF grants CCF-1514128, CCF-1733884, an Adobe research grant, and the Greek State Scholarships Foundation (IKY).
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Notes
- 1.
F2 source code available at https://github.com/ptheod/F2.git.
- 2.
This can be done by selecting a uniformly random permutation of size \([\mathtt {l}n]\) and using it to map each of the \(\mathtt {l}n\) non-zeros to equations; when \(\mathtt {l},\mathtt {r}\in O(1)\), the variables in each equation will be distinct with probability \(\varOmega (1)\), so that a handful of trials suffice to generate a matrix as desired.
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Acknowledgements
We are grateful to Kuldeep Meel and Moshe Vardi for sharing their code and formulas and for several valuable conversations. We thank Ben Sherman and Kostas Zampetakis for comments on earlier versions. Finally, we are grateful to the anonymous reviewers for several suggestions that improved the presentation.
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Achlioptas, D., Hammoudeh, Z., Theodoropoulos, P. (2018). Fast and Flexible Probabilistic Model Counting. In: Beyersdorff, O., Wintersteiger, C. (eds) Theory and Applications of Satisfiability Testing – SAT 2018. SAT 2018. Lecture Notes in Computer Science(), vol 10929. Springer, Cham. https://doi.org/10.1007/978-3-319-94144-8_10
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