Sparse polynomial interpolation, sparse linear system solving or modular rational reconstruction are fundamental problems in Computer Algebra. They come down to computing recurrence relations of a sequence with the Berlekamp–Massey algorithm. Likewise, multivariate interpolation and multidimensional cyclic code decoding require guessing sequence. Several algorithms solve this problem. The so-ca...

The paper presents, first, the Structural Blanks (SB) approach, then a method to compose loop programs. SB is an approach for expressing computations based on recurrence relations and focuses on data dependencies in loops. The paper presents language constructs and semantics for expressing programs that have complex data dependency patterns. These constructs are expressed using structural “blan...

We present an automatic method for computing tight upper bounds on the iteration number of special classes of program loops. These upper bounds are further used in the WCET analysis of programs. To do so, we refine program flows using SMT reasoning and rewrite multi-path loops into single-path ones. Single-path loops are further translated into a set of recurrence relations over program variabl...