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In this paper, we will describe how synchronous methods form the scientific basis for the creation of a correct-by-construction methodology required for safety-critical embedded systems. We will show how they are applied to software design, validation, and implementation through a process of high-level rigorous specifications, from which we can create correct-by-construction embeddable implementation. The synchronous methods we know today have more than 20 years of scientific research plus ten years of successful industrial application. This paper will explore the basic conceptual model of embedded computation supported by three underlying prerequisites: high-level rigorous graphical and textual languages, compiling algorithms for correct-by-construction implementation, and formal testing and verification techniques.