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We show that well-known instructions such as if then else, fork, join, while do, can be represented as row matrices or column-matrices. We define a matrix-instruction which encompasses and generalizes the above instructions. This instruction provides us with a compact tool for describing algorithms and for synthesizing them in synchronous and asynchronous structures. We show, e.g., that the synthesis of a program by means of elementary instructions reduces to the factorization of a matrix into elementary matrices. A formalism and a computation method are introduced which generalize the author's previous work on the subject.