Context-Sensitive Languages, Rational Graphs and Determinism
<|reference_start|>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.<br><br>   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.<|reference_end|>
@article{carayol2006context-sensitive,
    title={Context-Sensitive Languages, Rational Graphs and Determinism},
    author={Arnaud Carayol and Antoine Meyer},
    journal={Logical Methods in Computer Science, Volume 2, Issue 2 (July 19,
  2006) lmcs:2254},
    year={2006},
    doi={10.2168/LMCS-2(2:6)2006},
    archivePrefix={arXiv},
    eprint={cs/0606053},
    primaryClass={cs.LO}
}