Logical Description of Context-free Graph Languages (original) (raw)

Graph grammars and operational semantics

Theoretical Computer Science, 1982

Transformations of graphlike expressions are called correct if they preserve a given functional semantics of the expressions. Combining the algebraic theories of graph grammars (cf.

Finite graph automata for linear and boundary graph languages

Theoretical Computer Science, 2005

Graph grammars can be regarded as a generalization of context-free grammars from strings to graphs. Over the past 30 years a rich theory of graph grammars and their languages has been developed. However, there are no graph automata. There is no duality between generative and recognizing devices, as it is known for the Chomsky hierarchy of formal languages.

Graph Automata for Linear Graph Languages

Tagt, 1994

We introduce graph automata as devices for the recognition of linear graph languages. A graph automaton is the canonical extension of a nite state automaton recognizing a set of connected labeled graphs. It consists of a nite state control and a collection of heads, which search the input graph. In a move the graph automaton reads a new subgraph, checks some consistency conditions, changes states and moves some of its heads beyond the read subgraph. It proceeds such that the set of currently visited edges is an edge-separator between the visited and the yet undiscovered part of the input graph. Hence, the graph automaton realizes a graph searching strategy. Our main result states that nite graph automata recognize exactly the set of graph languages generated by connected linear NCE graph grammars.

Graph representation of context-free grammars

Computing Research Repository, 2007

In modern mathematics, graphs figure as one of the better-investigated class of mathematical objects. Various properties of graphs, as well as graph-processing algorithms, can be useful if graphs of a certain kind are used as denotations for CF-grammars. Furthermore, graph are well adapted to various extensions (one kind of such extensions being attributes).

On the concurrent semantics of Algebraic Graph Grammars

2005

Graph grammars are a powerful model of concurrent and distributed systems which can be seen as a proper extension of Petri nets. Inspired by this correspondence, a truly concurrent semantics has been developed along the years for the algebraic approaches to graph grammars, based on Winskel's style unfolding constructions as well as on suitable notions of processes.

Formal Verification of Graph Grammars using Mathematical Induction

Electronic Notes in Theoretical Computer Science, 2009

Graph grammars are a formal description technique suitable for the specification of distributed and reactive systems. Model-checking of graph grammars is currently supported by various approaches. However, in many situations the use of this technique can be very time and space consuming, hindering the verification of properties of many systems. This work proposes a relational and logical approach to graph grammars that allows formal verification of systems using mathematical induction. We use relational structures to define graph grammars and first-order logic to model graph transformations. This approach allows proving properties of systems with infinite state-spaces.