Abstract

This paper presents empirical evidence of a satisfiability threshold in random 3CNF formulas. The paper also expands on and supports the conjecture of Mitchell, Selman, and Levesque [13] that hard randomly generated CNF formulas will be hard for any reasonable satisfiability algorithm. We report statistics for a much larger set of variables than have been previously reported; in particular, we show that for each clause to variable ratio less than 4.2, the percentage of satisfiable formulas increases, and for each clause to variable ratio greater than 4.2, the percentage of satisfiable formulas decreases as a function of number of variables. We found that several algorithms behaved qualitatively in the same fashion. We report on the relative performance of each algorithm. Keywords: backtracking, logic, reasoning, satisfiability, threshold behavior

Citations