Deriving Small Unsatisfiable Cores with Dominators

  • Roman Gershman
  • Maya Koifman
  • Ofer Strichman
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4144)


The problem of finding a small unsatisfiable core of an unsatisfiable CNF formula is addressed. The proposed algorithm, Trimmer, iterates over each internal node d in the resolution graph that ‘consumes’ a large number of clauses M (i.e. a large number of original clauses are present in the unsat core only for proving d) and attempts to prove them without the M clauses. If this is possible, it transforms the resolution graph into a new graph that does not have the M clauses at its core. Trimmer can be integrated into a fixpoint framework similarly to Malik and Zhang’s fix-point algorithm (run_till_fix). We call this option trim_till_fix. Experimental evaluation on a large number of industrial CNF unsatisfiable formulas shows that trim_till_fix doubles, on average, the number of reduced clauses in comparison to run_till_fix. It is also better when used as a component in a bigger system that enforces short timeouts.


Sink Node Small Core Unit Clause Resolution Step Empty Clause 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Roman Gershman
    • 1
  • Maya Koifman
    • 1
  • Ofer Strichman
    • 1
  1. 1.TechnionHaifaIsrael

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