Hyperedge Replacement: Grammars and Languages

The area of graph grammars is theoretically attractive and
well motivated byvarious applications. More than 20 years
ago, the concept of graph grammars was introduced by A.
Rosenfeld as a formulation of some problems in pattern
recognition and image processing, as well as by H.J.
Schneider as a method for data type specification. Within
graph-grammar theory one maydistinguish the set-theoretical
approach, the algebraic approach, and the logical approach.
These approaches differ in the method in which graph
replacement is described. Specific approaches,
node replacement and hyperedge replacement, concern the
basic units of a hypergraph, nodes and hyperedges.
This monograph is mainly concerned with the
hyperedge-replacement approach. Hyperedge-replacement
grammars are introduced as a device for generating
hypergraph languages including graph languages and string
languages. The concept combines a context-free rewriting
with a comparatively large generative power. The volume
includes a foreword by H. Ehrig.