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chapters/process.tex

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\chapter{Occurrence Graph Grammars with NACs}\label{ch:process}
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Occurrence Graph Grammars (OGGs) were defined for the Single-Pushout (SPO) approach by~\cite{Ribeiro1996}, and for the Double-Pushout (DPO) approach by~\cite{Corradini1996}. In both cases they consist of a way of representing the concurrent semantics of a graph grammar as a graph grammar itself.
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Occurrence Graph Grammars (OGGs) were defined for the Single-Pushout (SPO) approach by~\cite{Ribeiro1996}, and for the Double-Pushout (DPO) approach by~\cite{Corradini1996}. In both cases they consist of a way of representing the concurrent semantics of a graph grammar as a graph grammar itself. It also presents the advantage of having a more compact structure than other semantic models for graph grammars.
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For example, with Unfolding~\cite{Ribeiro1996} the semantics of a graph grammar is given by the set of all possible derivations of that grammar, which may be an infinite structure, whereas with OGGs we have a grammar which already encodes such derivations in a finite way.
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The aim of an OGG is to describe all possible states and changes of states of the graph grammar from which it was constructed.
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This is possible because occurrence grammars can be regarded as an execution history of the underlying grammar.

thesis.tex

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Finalmente, para mainha, Dona Necila... eu jamais poderei expressar suficientemente o quão a senhora foi importante em todas as minhas conquistas até agora. A senhora sempre foi a pessoa que mais admiro na vida, por toda sua luta, dedicação e sacrifícios para dar a mim e aos meus irmãos todas as oportunidades que a senhora não teve. Esse mestrado é tão seu quanto meu. Vou te amar pra sempre.
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\begin{abstract}
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Graph Grammars are based on the application of rules that are able to modify graphs, as such, they provide a suitable formalism to model complex systems in an intuitive and precise manner, providing both a graphical, straightforward language and a solid formal background for systems analysis. Therefore, they have been used in a wide range of applications within Computer Science, specially in the field of Model-Driven Development.
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Graph Grammars are based on the application of rules that are able to modify graphs, as such, they provide a suitable formalism to model complex systems in an intuitive and precise manner, providing both a graphical language and a solid formal background for systems analysis. Therefore, they have been used in a wide range of applications within Computer Science, specially in the field of Model-Driven Development.
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Particularly, the study of the Semantics of Graph Grammars, i.e. which graphs belong to the language of a grammar and which derivations are possible within the context of a grammar, provides a powerful framework for reasoning about the execution behaviour of systems modelled as Graph Grammars.
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There are several different ways of specifying the Semantics of Graph Grammars.
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One notable possibility is the use of Occurrence Graph Grammars, which encodes the Semantics in a structure that is also a Graph Grammar itself. Occurrence Graph Grammars were introduced in the nineties and used ever since, however the original definitions lack the inclusion of Negative Application Conditions, additional structures imposed over the rules of a grammar to better tune their possible applications according to the execution context.
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One notable possibility is the use of Occurrence Graph Grammars, which encodes the Semantics in a structure that is also a Graph Grammar itself. Occurrence Graph Grammars differ from other semantic models such as Unfolding and Canonical Derivations mainly by providing a more compact, easier to analyse structure. They were introduced in the nineties and used ever since, however the original definitions lack the inclusion of Negative Application Conditions, additional structures imposed over the rules of a grammar to better tune their possible applications according to the execution context.
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Given the important role Negative Application Conditions play in the modelling and analysis of complex systems as Graph Grammars nowadays, this thesis presents an extension of the framework of Occurrence Graph Grammars to include them. It also presents its implementation in Verigraph, a system specification and verification tool based on graph rewriting.
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\end{abstract}
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