4 research outputs found
Inferring Chemical Reaction Patterns Using Rule Composition in Graph Grammars
Modeling molecules as undirected graphs and chemical reactions as graph
rewriting operations is a natural and convenient approach tom odeling
chemistry. Graph grammar rules are most naturally employed to model elementary
reactions like merging, splitting, and isomerisation of molecules. It is often
convenient, in particular in the analysis of larger systems, to summarize
several subsequent reactions into a single composite chemical reaction. We use
a generic approach for composing graph grammar rules to define a chemically
useful rule compositions. We iteratively apply these rule compositions to
elementary transformations in order to automatically infer complex
transformation patterns. This is useful for instance to understand the net
effect of complex catalytic cycles such as the Formose reaction. The
automatically inferred graph grammar rule is a generic representative that also
covers the overall reaction pattern of the Formose cycle, namely two carbonyl
groups that can react with a bound glycolaldehyde to a second glycolaldehyde.
Rule composition also can be used to study polymerization reactions as well as
more complicated iterative reaction schemes. Terpenes and the polyketides, for
instance, form two naturally occurring classes of compounds of utmost
pharmaceutical interest that can be understood as "generalized polymers"
consisting of five-carbon (isoprene) and two-carbon units, respectively
Multi-amalgamation of rules with application conditions in M-adhesive categories
Dieser Beitrag ist mit Zustimmung des Rechteinhabers aufgrund einer (DFG geförderten) Allianz- bzw. Nationallizenz frei zugänglich.This publication is with permission of the rights owner freely accessible due to an Alliance licence and a national licence (funded by the DFG, German Research Foundation) respectively.Amalgamation is a well-known concept for graph transformations that is used to model synchronised parallelism of rules with shared subrules and corresponding transformations. This concept is especially important for an adequate formalisation of the operational semantics of statecharts and other visual modelling languages, where typed attributed graphs are used for multiple rules with nested application conditions. However, the theory of amalgamation for the double-pushout approach has so far only been developed on a set-theoretical basis for pairs of standard graph rules without any application conditions. For this reason, in the current paper we present the theory of amalgamation for M-adhesive categories, which form a slightly more general framework than (weak) adhesive HLR categories, for a bundle of rules with (nested) application conditions. The two main results are the Complement Rule Theorem, which shows how to construct a minimal complement rule for each subrule, and the Multi-Amalgamation Theorem, which generalises the well-known Parallelism and Amalgamation Theorems to the case of multiple synchronised parallelism. In order to apply the largest amalgamated rule, we use maximal matchings, which are computed according to the actual instance graph. The constructions are illustrated by a small but meaningful running example, while a more complex case study concerning the firing semantics of Petri nets is presented as an introductory example and to provide motivation
Multi-amalgamation of rules with application conditions in M-adhesive categories
Dieser Beitrag ist mit Zustimmung des Rechteinhabers aufgrund einer (DFG geförderten) Allianz- bzw. Nationallizenz frei zugänglich.This publication is with permission of the rights owner freely accessible due to an Alliance licence and a national licence (funded by the DFG, German Research Foundation) respectively.Amalgamation is a well-known concept for graph transformations that is used to model synchronised parallelism of rules with shared subrules and corresponding transformations. This concept is especially important for an adequate formalisation of the operational semantics of statecharts and other visual modelling languages, where typed attributed graphs are used for multiple rules with nested application conditions. However, the theory of amalgamation for the double-pushout approach has so far only been developed on a set-theoretical basis for pairs of standard graph rules without any application conditions. For this reason, in the current paper we present the theory of amalgamation for M-adhesive categories, which form a slightly more general framework than (weak) adhesive HLR categories, for a bundle of rules with (nested) application conditions. The two main results are the Complement Rule Theorem, which shows how to construct a minimal complement rule for each subrule, and the Multi-Amalgamation Theorem, which generalises the well-known Parallelism and Amalgamation Theorems to the case of multiple synchronised parallelism. In order to apply the largest amalgamated rule, we use maximal matchings, which are computed according to the actual instance graph. The constructions are illustrated by a small but meaningful running example, while a more complex case study concerning the firing semantics of Petri nets is presented as an introductory example and to provide motivation