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Status: Unchecked ×Keyword: unsatisfiability ×Clear all

3 claims from 1 paper

1. Computer Science › Constraint Satisfaction and Optimization

   Heuristic average-case analysis of the backtrack resolution of random 3-satisfiability instances

   Cocco and Monasson · Theoretical Computer Science · 2004

   The paper analyses how long backtrack algorithms take on random 3-SAT instances, identifying three regimes by clause-to-variable ratio and estimating the exponential cost where search is hard.

   Unchecked3 claims
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   1. UncheckedFor random 3-SAT puzzles with few clauses per variable, the DPLL search algorithm almost surely finds a solution in time growing linearly with the number of variables.“Lower sat phase: for small ratios, DPLL almost surely finds a solution in a time growing linearly with the number N of variables.”
   2. UncheckedFor random 3-SAT puzzles with a medium ratio of clauses to variables, a solution almost surely exists, but the DPLL algorithm usually needs exponential time to find it.“Upper sat phase: for intermediate ratios, instances are almost surely satisfiable but finding a solution requires exponential time (2 ^ (N omega) with omega>0) with high probability.”
   3. UncheckedFor random 3-SAT puzzles with many clauses per variable, there is almost always no solution, and backtracking proofs of this take exponential time.“Unsat phase: for large ratios, there is almost always no solution and proofs of refutation are exponential.”