We are concerned here with Smale (i.e. $C^1$-structurally
stable) diffeomorphisms of compact
surfaces. Bonatti and Langevin have produced some
descriptions of the dynamics of any
such diffeomorphism (). Actually, each
admits infinitely many different
combinatorial descriptions. The aim of the present article is to
describe an algorithm which decides
whether two combinatorial descriptions correspond to the
diffeomorphism or not.
This provides an algorithmic way to classify Smale
of surfaces up to topological conjugacy (on canonical
of the basic pieces).