Breaking the PPSZ Barrier for Unique 3-SAT

  • Timon Hertli
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8572)


The PPSZ algorithm by Paturi, Pudlák, Saks, and Zane (FOCS 1998) is the fastest known algorithm for (Promise) Unique k-SAT. We give an improved algorithm with exponentially faster bounds for Unique 3-SAT.

For uniquely satisfiable 3-CNF formulas, we do the following case distinction: We call a clause critical if exactly one literal is satisfied by the unique satisfying assignment. If a formula has many critical clauses, we observe that PPSZ by itself is already faster. If there are only few clauses in total, we use an algorithm by Wahlström (ESA 2005) that is faster than PPSZ in this case. Otherwise we have a formula with few critical and many non-critical clauses. Non-critical clauses have at least two literals satisfied; we show how to exploit this to improve PPSZ.


Success Probability Randomized Algorithm Satisfying Assignment Promise Problem Satisfying Truth Assignment 
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© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Timon Hertli
    • 1
  1. 1.Institute for Theoretical Computer Science, Department of Computer ScienceETH ZürichSwitzerland

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