Many powerful parallelizing compiling techniques rely on the logic structures of arrays. However, in real applications, lots of arrays are flat one-dimensional arrays and hence may disable some compiling optimizations. This paper presents a new framework and algorithms for guessing the logical multi-dimensional array structures from the flat one-dimensional arrays automatically, and makes powerful compiling optimizations possible. We first give a lemma that points out the basic property which the guessed multi-dimensional arrays should satisfy, then based on this lemma we give two basic rules that should be followed in guessing logic structures of arrays, and finally based on the two rules we present the algorithms for guessing logic structures of arrays. The experimental results show the algorithms for guessing the logical multi-dimensional array structures are effective.