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Competitive Sorter-based Encoding of PB-Constraints into SAT

14 pagesPublished: March 15, 2019


A Pseudo-Boolean (PB) constraint is a linear inequality constraint over Boolean variables. A popular idea to solve PB-constraints is to transform them to CNFs (via BDDs, adders and sorting networks [5, 11]) and process them using – increasingly improving – state-of-the-art SAT-solvers. Recent research have favored the approach that uses Binary Decision Diagrams (BDDs), which is evidenced by several new constructions and optimizations [2, 21]. We show that encodings based on comparator networks can still be very competitive. We present a system description of a PB-solver based on MiniSat+ [11] which we extended by adding a new construction of selection network called 4-Way Merge Selection Network, with a few optimizations based on other solvers. Experiments show that on many instances of popular benchmarks our technique outperforms other state-of-the-art PB-solvers.

Keyphrases: comparator network, Constraints Solver, odd-even network, Pseudo-Boolean, SAT, selection network

In: Daniel Le Berre and Matti Järvisalo (editors). Proceedings of Pragmatics of SAT 2015 and 2018, vol 59, pages 65--78

BibTeX entry
  author    = {Micha\{\textbackslash{}l\} Karpi\textbackslash{}'nski and Marek Piotr\textbackslash{}'ow},
  title     = {Competitive Sorter-based Encoding of PB-Constraints into SAT},
  booktitle = {Proceedings of Pragmatics of SAT 2015 and 2018},
  editor    = {Daniel Le Berre and Matti J\textbackslash{}"arvisalo},
  series    = {EPiC Series in Computing},
  volume    = {59},
  pages     = {65--78},
  year      = {2019},
  publisher = {EasyChair},
  bibsource = {EasyChair,},
  issn      = {2398-7340},
  url       = {},
  doi       = {10.29007/hh3v}}
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