Theoretical Computer Science
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
Handbook of graph grammars and computing by graph transformation: vol. 3: concurrency, parallelism, and distribution
Specification of Graph Translators with Triple Graph Grammars
WG '94 Proceedings of the 20th International Workshop on Graph-Theoretic Concepts in Computer Science
Equations and rewrite rules: a survey
Equations and rewrite rules: a survey
Fundamentals of Algebraic Graph Transformation (Monographs in Theoretical Computer Science. An EATCS Series)
Matrix approach to graph transformation: matching and sequences
ICGT'06 Proceedings of the Third international conference on Graph Transformations
Matrix Graph Grammars with Application Conditions
Fundamenta Informaticae
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In this paper we present a new approach for the analysis of rule-based specification of system dynamics. We model system states as simple digraphs, which can be represented with boolean matrices. Rules modelling the different state changes of the system can also be represented with boolean matrices, and therefore the rewriting is expressed using boolean operations only. The conditions for sequential independence between pair of rules are well-known in the categorical approaches to graph transformation (e.g. single and double pushout). These conditions state when two rules can be applied in any order yielding the same result. In this paper, we study the concept of sequential independence in our framework, and extend it in order to consider derivations of arbitrary finite length. Instead of studying one-step rule advances, we study independence of rule permutations in sequences of arbitrary finite length. We also analyse the conditions under which a sequence is applicable to a given host graph. We introduce rule composition and give some preliminary results regarding parallel independence. Moreover, we improve our framework making explicit the elements which, if present, disable the application of a rule or a sequence.