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Parallelization of SAT Algorithms on GPUs [pdf] (inesc-id.pt)
65 points by setra 333 days ago | hide | past | web | favorite | 18 comments

This approach is unworkable, it has been demonstrated many times. I have not only been developing a SAT solver for >7 years (with >9000 commits) but also have participated in the SAT competition in all these years. I used to get a proposal like this a lot (thankfully, they dried up). None of them made it work. I used to work on programming GPGPUs in a professional setting, (rainbow table generators&lookup systems), so I'm not unfamiliar with their advantages and restrictions.

This approach is unworkable because: * propagation needs modification of the watchlist (or it needs to have all literals of all clauses attached, which is incredibly slow and also unworkable) * propagation is actually only about 50-60% of what a solver is doing: conflict resolution, clause database management and inprocessing takes a lot of time * propagation is hard to parallelize as you need to update a global data structure of propagated literals and then act on that * etc

This proposal will not work (and I sure it did not, if it was ever tried) and I don't understand how it got this high at ycombinator. If you want to look at good SAT solvers, look at lingeling, COPMinisat, MiniSat, or CryptoMiniSat. You may learn a lot from them. Easy starting is MiniSat. Good luck :)

> I don't understand how it got this high at ycombinator

Oh that's easy: because most of us know nothing about SAT solvers other than (maybe) what they are and that they're cool. We need people like you to teach us, so I'm glad you showed up! (A great example of https://meta.wikimedia.org/wiki/Cunningham's_Law.)

   If you want to look at good SAT 
   solvers, look ... CryptoMiniSat.
Any personal relationship with CryptoMiniSat? ;)

Considering that CryptoMiniSat got 3rd place (after 1st and 2nd both being lingeling) in Parallel SAT solving the last competition, I think it was fair to include it. Sure, it's mine, but I also put it at the end :) Other solvers that are good to look at: glucose and riss. Note that a lot of solvers are variations of MiniSat. riss, ligeling, PrecoSat and CryptoMiniSat are the only ones that substantially differ from MiniSat.

Thanks for the recommendations. I love SAT solvers and have been looking for a way to get into them.

Google does not know "COPMinisat", would you please clarify?

PicoSAT is also small and easy to embed, however in CryptoMiniSat we trust, thank you very much!

Sorry, wanted to say CoMiniSatPS, here:


One of its variants won the Main track of the SAT Competition of 2016, see


For all the solvers' source codes, see


Please, do you have any recommendations for books about SAT solving for beginners?

There is quite a bit of work on parallelising SAT solving, as it's one of the most important algorithmic problems, both in theory and in practise, but (as far as I'm aware) the top sequential algorithms still beat parallel solvers. The most successful approach at this point seems to be Cube-and-Conquer [1], but I don't think this is considered a good approach in itself. There is a huge amount of scope for new ideas. I doubt that anything naive will work, as SAT solving is a rather competitive research field.

The annual SAT competition http://www.satcompetition.org has a track for parallel solving.

See [2, 3, 4] for an overview of the field.

[1] M. J. H. Heule, O. Kullmann, S. Wieringa, A. Biere, Cube and Conquer: Guiding CDCL SAT Solvers by Lookaheads.

[2] S. Hölldobler, N. Manthey, V. H. Nguyen, J. Stecklina, P. Steinke, A Short Overview on Modern Parallel SAT-Solvers.

[3] S. Wieringa, K. Heljanko, Asynchronous Multi-Core Incremental SAT Solving.

[4] Y. Hamadi, C. M. Wintersteiger, Seven Challenges in Parallel SAT Solving.

Here's a non-paywalled link to [2] if anyone else is looking for it: http://www.ki.inf.tu-dresden.de/~norbert/webdata/publication...

the top sequential algorithms still beat parallel solvers

Wow, that's interesting! Are there any other examples where a sequential algorithm beats a parallel one?

It is an open question whether there exist algorithms that cannot be parallelized. Some that are most likely to be inherently sequential are listed here: https://en.wikipedia.org/wiki/P-complete#P-complete_problems

SAT solvers and neural networks are probably the most curious software technologies around. Both attempt to solve NP-complete problems (learning and SAT). Both are still largely based on 1960s algorithms (backpropagation for NNs and DPLL for SAT) made surprisingly useful in practice by advances in hardware and heuristics accumulated over the years. Both are mysterious from a theoretical point of view, with little progress in our theoretical understanding of why they work well in practice and how we can come up with better algorithms.

This article by Moshe Vardi[1] and this one by Dick Lipton[2] are a nice introduction to the mystery of SAT solvers.

[1]: http://cacm.acm.org/magazines/2014/3/172516-boolean-satisfia...

[2]: https://rjlipton.wordpress.com/2009/07/13/sat-solvers-is-sat...

This is a proposed work for a Master's thesis. It seems to be from 2013, so I wonder whether it was successful?

If I had to guess, I would think implementing a SAT solver on a GPU is quite hard. Many branches etc.

Look at http://algos.inesc-id.pt/~pff/projects/parsat/?Publications

It seems Mr Costa has graduated, but the link to his thesis points to an empty pdf.

It would be interesting to apply probabilistic algorithms for SAT solving in GPUs

Publish or perish leaves very little room for sanity checks once your window of graduation starts to close.

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