Structurally synthesized binary decision diagrams (SSBDD) are a special type of BDDs that are generated by superposition according to the structure of propositional formula. Fast algorithms for simulation, diagnostic reasoning and test generation running on SSBDDs exploit their specific properties. Hence the correctness of SSBDDs should be checked before using those algorithms. The problem of recognizing SSBDDs can be reduced to the problem of recognizing their skeleton, namely superpositional graphs, which are a proper subclass of binary graphs. This paper presents linear time algorithms for testing whether a binary graph is a superpositional graph and for restoring the history of its generating process.

The class of superpositional graphs, which is defined as the set of graphs whose elements are generated by superposition, is a subclass of binary graphs. The properties of superpositional graphs are investigated, and necessary and sufficient conditions found for a binarygraph to be a superpositional graph.

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