Redundancy and subsumption in high-level replacement systems

System verification in the broadest sense deals with those semantic properties that can be decided or deduced by analyzing a syntactical description of the system. Hence, one may consider the notions of redundancy and subsumption in this context as they are known from the area of rule-based systems. A rule is redundant if it can be removed without affecting the semantics of the system; it is subsumed by another rule if each application of the former one can be replaced by an application of the latter one with the same effect. In this paper, redundancy and subsumption are carried over from rule-based systems to high-level replacement systems, which in turn generalize graph and hypergraph grammars. The main results presented in this paper are a characterization of subsumption and a sufficient condition for redundancy, which involves composite productions.Postprint (published version

Typing of Graph Transformation Units

The concept of graph transformation units in its original sense is a structuring principle for graph transformation systems which allows the interleaving of rule applications with calls of imported units in a controlled way. The semantics of a graph transformation unit is a binary relation on an underlying type of graphs. In order to get a flexible typing mechanism for transformation units and a high degree of parallelism this paper introduces typed graph transformation units that transform k-tuples of typed input graphs into l-tuples of typed output graphs in a controlled and structured way. The transformation of the typed graph tuples is performed with actions that apply graph transformation rules and imported typed units simultaneously to the graphs of a tuple. The transformation process is controlled with control conditions and with graph tuple class expressions. The new concept of typed graph transformation units is illustrated with examples from the area of string parsing with finite automata

Redundancy and subsumption in high-level replacement systems

System verification in the broadest sense deals with those semantic properties that can be decided or deduced by analyzing a syntactical description of the system. Hence, one may consider the notions of redundancy and subsumption in this context as they are known from the area of rule-based systems. A rule is redundant if it can be removed without affecting the semantics of the system; it is subsumed by another rule if each application of the former one can be replaced by an application of the latter one with the same effect. In this paper, redundancy and subsumption are carried over from rule-based systems to high-level replacement systems, which in turn generalize graph and hypergraph grammars. The main results presented in this paper are a characterization of subsumption and a sufficient condition for redundancy, which involves composite productions

Graph Transformation Units Guided by a SAT Solver

Graph transformation units are rule-based devices to model graph algorithms, graph processes, and the dynamics of systems the states of which are represented by graphs. Given a graph, various rules are applicable at various matches in general, but not any choice leads to a proper result so that one faces the problem of nondeterminism. As countermeasure, graph transformation units provide the generic concept of control conditions which allow one to cut down the nondeterminism and to choose the proper rule applications out of all possible ones. In this paper, we propose an alternative approach. For a special type of graph transformation units including the solution of many NP-complete and NP-hard problems, the successful derivations from initial to terminal graphs are described by propositional formulas. In this way, it becomes possible to use a SAT solver to find out whether there is a successful derivation for some initial graph or not and how it is built up in the positive case

Handbook of graph grammars and computing by graph transformation

Graph grammars originated in the late 60s, motivated by considerations about pattern recognition and compiler construction. Since then, the list of areas which have interacted with the development of graph grammars has grown quite impressively. Besides the aforementioned areas, it includes software specification and development, VLSI layout schemes, database design, modeling of concurrent systems, massively parallel computer architectures, logic programming, computer animation, developmental biology, music composition, visual languages, and many others.The area of graph grammars and graph tra