The paper considers a family of formal grammars that extends linear context-free grammars with an operator for referring to the left context of a substring being defined, as well as with a conjunction operation (as in linear conjunctive grammars). These grammars are proved to be computationally equivalent to an extension of one-way real-time cellular automata with an extra data channel. The main result is the undecidability of the emptiness problem for grammars restricted to a one-symbol alphabet, which is proved by simulating a Turing machine by a cellular automaton with feedback. The same construction proves the σ02-completeness of the finiteness problem for these grammars. © 2014 Springer-Verlag Berlin Heidelberg.
CITATION STYLE
Barash, M., & Okhotin, A. (2014). Linear grammars with one-sided contexts and their automaton representation. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 8392 LNCS, pp. 190–201). Springer Verlag. https://doi.org/10.1007/978-3-642-54423-1_17
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