From Hyperedge Replacement to Separation Logic and Back

Hyperedge-replacement grammars and separation-logic formulas both define classes of graph-like structures. In this paper, we relate the different formalisms by effectively translating restricted hyperedge-replacement grammars into formulas of a fragment of separation-logic with recursive predicates, and vice versa. The translations preserve the classes of specified graphs, and hence the two approaches are of equivalent power. It follows that our fragment of separation-logic inherits properties of hyperedge-replacement grammars, such as inexpressibility results. We also show that several operators of full separation logic cannot be expressed using hyperedge replacement.