In this work, we describe how the preservation of value-equivalence of variables can be proved based on translation validation of synchronous data-flow value-graphs. It focuses on proving that every output variables in the original program and their counterparts in the transformed program, the generated C code, have the same values. The computation of each output variable and its counterpart is represented by a formal representation, a shared value-graph. This graph deterministically represents the computation of the output in the original program and its counterpart in the transformed program, and the nodes for the common variables have been shared in the graph. Given a SDVG, support that we want to show that the two output variables have the same value. We simply need to check that they are represented by graphs which are rooted at the same graph node. We manage to make the check by normalizing SDVGs by some rewrite rules.
