Addendum to the Article “Types vs. PDGs in Information Flow Analysis” – Proofs and Operational Semantics

Before proving Lemma 1 from [MS13] we prove several propositions that relate paths in the graph PDG(CFG c ) where c is of the form if (e) then c1 else c2 fi, while (e) do c1 od, or c1; c2 to paths in the graphs PDG(CFG I,O c1 ) and (if applicable) PDG(CFG c2 ). In the proofs, we write p + k for the path that is obtained from p by adding k to each node on p that is a natural number, and leaving start and stop unchanged. Moreover, we write p−k for the path that is obtained from p by subtracting k from each node on p that is a natural number, and leaving start and stop unchanged.