Graph Transformation Units Guided by a SAT Solver

• Published in: Graph Transformations pp. 27 - 42
• Main Authors: Kreowski, Hans-Jörg, Kuske, Sabine, Wille, Robert
• Format: Book Chapter
• Language: English
• Published: Berlin, Heidelberg Springer Berlin Heidelberg 2010
• Series: Lecture Notes in Computer Science
• Subjects: Graph Transformation; Propositional Formula; Regular Expression; Rule Application; Transformation Unit
• ISBN: 9783642159275; 3642159273
• ISSN: 0302-9743; 1611-3349
• DOI: 10.1007/978-3-642-15928-2_3

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.