This recursion is guided by the structure of a graph of translation tables that help compartmentalize the scope of various functions and identifier spaces, while relating these spaces for resource discovery, resolution, and routing.
The graphs represent translation and rotation along the x-axis.
We build a massive translation graph, automatically constructed from over 630 machine-readable dictionaries and Wiktionaries.
The construction of a simple back-translation graph for the amino acid R is illustrated in Figure 2.
The space necessary for storing the back-translation graph of a protein sequence P of size n depends linearly on n.
Consequently, the overall memory consumption for storing the back-translation graph of a protein sequence P of size n is (n).
The reverse complementary of a back-translation graph can be obtained in a classic manner, by reversing the arcs and complementing the nucleotide symbols that label the nodes, as illustrated in Figure 3.
Basically, as mentioned in the section dedicated to data structures, the back-translation graph G P = (V P, E P ) consists of 3· n groups of nodes (as each of the n amino-acids are encoded by sequences of 3 nucleotides).
Also, as the scoring system we propose in this paper requires to differentiate identical symbols by their context, identical nucleotides appearing at the third position of different codons for amino acids L, S and R will have different corresponding nodes in the back-translation graph.
More formally, a back-translation graph of an amino acid sequence P of length n is a directed acyclic graph G P = (V P, E P ) where: (1) where are the nucleotide symbols that appear at position i in at least one of the protein's putative coding sequences, and (2) are arcs between nodes corresponding to symbols that are consecutive in one of the protein's putative coding sequences.
