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Context-Sensitive Languages, Rational Graphs and Determinism

By Arnaud Carayol and Antoine Meyer

Abstract

24 pagesInternational audienceWe 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

Topics: language theory, infinite graphs, automata, determinism, ACM: F.1.1 Models of Computation, F.4.3 Formal Languages, [INFO.INFO-LO] Computer Science [cs]/Logic in Computer Science [cs.LO]
Publisher: Logical Methods in Computer Science Association
Year: 2006
DOI identifier: 10.2168/LMCS-2(2:6)2006
OAI identifier: oai:HAL:hal-00149086v1
Provided by: Hal-Diderot
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