Graph grammars and the complexity gap in the isomorphism problem for acyclic digraphs

Abstract

We regard several classes of acyclic digraphs forming a hierarchy, which represents the present complexity gap in the isomorphism problem for acyclic digraphs. The classes at the lowest level of the hierarchy have a polynomially solvable isomorphism problem, whereas the more general ones have an isomorphism complete one. For all classes we develop graph grammars and examine them for properties reflecting the complexity of the corresponding isomorphism problem.