  The probability P(alpha, N) that search algorithms for random Satisfiability
problems successfully find a solution is studied as a function of the ratio
alpha of constraints per variable and the number N of variables. P is shown to
be finite if alpha lies below an algorithm--dependent threshold alpha\_A, and
exponentially small in N above. The critical behaviour is universal for all
algorithms based on the widely-used unitary propagation rule: P[ (1 + epsilon)
alpha\_A, N] ~ exp[-N^(1/6) Phi(epsilon N^(1/3)) ]. Exponents are related to
the critical behaviour of random graphs, and the scaling function Phi is
exactly calculated through a mapping onto a diffusion-and-death problem.
