Contextual graph grammars characterising Rational Graphs

International audienceDeterministic graph grammars generate a family of infinite graphs which characterise context-free (word) languages. The present paper introduces a context-sensitive extension of these grammars. We prove that this extension characterises rational graphs (whose traces are context-sensitive languages). We illustrate that this extension is not straightforward: the most obvious context-sensitive graph rewriting systems generate non recursive infinite graphs

Context-Sensitive Languages, Rational Graphs and Determinism

We investigate families of infinite automata for context-sensitive languages. An infinite automaton is an infinite labeled graph with two sets of initial and final vertices. Its language is the set of all words labelling a path from an initial vertex to a final vertex. In 2001, Morvan and Stirling proved that rational graphs accept the context-sensitive languages between rational sets of initial and final vertices. This result was later extended to sub-families of rational graphs defined by more restricted classes of transducers. languages. Our contribution is to provide syntactical and self-contained proofs of the above results, when earlier constructions relied on a non-trivial normal form of context-sensitive grammars defined by Penttonen in the 1970's. These new proof techniques enable us to summarize and refine these results by considering several sub-families defined by restrictions on the type of transducers, the degree of the graph or the size of the set of initial vertices

Context-sensitive languages, rational graphs and determinism

Vol. 2 (2:6) 2006, pp. 1–24 www.lmcs-online.or