Compile-time program analysis aims to extract from a program properties useful for efficient implementations and sofware verification. A property of interest is the computational semantics of a program. For decidability reasons, only an approximation of this semantics can be computed. Set-based analysis [Hei92a] provides an elegant and accurate method for this. In the logic programming framework, this computation can be related to type inference [MR85]. In [FSVY91], a simpler presentation based on program transformation and algorithms on alternating tree automata is proposed. Unfortunately, the authors focussed on type checking (i.e. a membership test to the approximate semantics). We propose in this paper a new method to achieve set-based analysis reusing the main transformation described in [FSV Y91]. The main tool for both computation and representation of the result of set-based analysis is tree automata. This leads to a global and coherent presentation of the problem of set-based analysis combined with the simplicity of [FSVY91]. We obtain also a complexity characterization for the problem and our method. We expect that this tree automaton approach will lead to an efficient implementation, contrary to the first conclusions of [FSVY91].