Theoretical Computer Science
Handbook of graph grammars and computing by graph transformation: volume I. foundations
Handbook of graph grammars and computing by graph transformation: volume I. foundations
Node replacement graph grammars
Handbook of graph grammars and computing by graph transformation
Algebraic approaches to graph transformation. Part I: basic concepts and double pushout approach
Handbook of graph grammars and computing by graph transformation
Handbook of graph grammars and computing by graph transformation
The expression of graph properties and graph transformations in monadic second-order logic
Handbook of graph grammars and computing by graph transformation
AToM3: A Tool for Multi-formalism and Meta-modelling
FASE '02 Proceedings of the 5th International Conference on Fundamental Approaches to Software Engineering
Confluence of Typed Attributed Graph Transformation Systems
ICGT '02 Proceedings of the First International Conference on Graph Transformation
Fundamentals of Algebraic Graph Transformation (Monographs in Theoretical Computer Science. An EATCS Series)
Electronic Notes in Theoretical Computer Science (ENTCS)
Correctness of high-level transformation systems relative to nested conditions†
Mathematical Structures in Computer Science
Nested constraints and application conditions for high-level structures
Formal Methods in Software and Systems Modeling
Nested quantification in graph transformation rules
ICGT'06 Proceedings of the Third international conference on Graph Transformations
Matrix approach to graph transformation: matching and sequences
ICGT'06 Proceedings of the Third international conference on Graph Transformations
Satisfiability of high-level conditions
ICGT'06 Proceedings of the Third international conference on Graph Transformations
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In the Matrix approach to graph transformation we represent simple digraphs and rules with Boolean matrices and vectors, and the rewriting is expressed using Boolean operators only. In previous works, we developed analysis techniques enabling the study of the applicability of rule sequences, their independence, state reachability and the minimal graph able to fire a sequence. In the present paper we improve our framework in two ways. First, we make explicit (in the form of a Boolean matrix) some negative implicit information in rules. This matrix (called nihilation matrix) contains the elements that, if present, forbid the application of the rule (i.e. potential dangling edges, or newly added edges, which cannot be already present in the simple digraph). Second, we introduce a novel notion of application condition, which combines graph diagrams together with monadic second order logic. This allows for more flexibility and expressivity than previous approaches, as well as more concise conditions in certain cases. We demonstrate that these application conditions can be embedded into rules (i.e. in the left hand side and the nihilation matrix), and show that the applicability of a rule with arbitrary application conditions is equivalent to the applicability of a sequence of plain rules without application conditions. Therefore, the analysis of the former is equivalent to the analysis of the latter, showing that in our framework no additional results are needed for the study of application conditions. Moreover, all analysis techniques of [21,22] for the study of sequences can be applied to application conditions.