Ricerc@Sapienza

We investigate the space complexity of refuting 3-CNFs in Resolution and algebraic systems. We prove that every Polynomial Calculus with Resolution refutation of a random 3-CNF ? in n variables requires, with high probability, distinct monomials to be kept simultaneously in memory. The same construction also proves that every Resolution refutation of ? requires, with high probability, clauses each of width to be kept at the same time in memory. This gives a lower bound for the total space needed in Resolution to refute ?. These results are best possible (up to a constant factor) and answer questions about space complexity of 3-CNFs.