Linear Grammars with One-Sided Contexts and Their Automaton Representation [chapter]

Mikhail Barash, Alexander Okhotin
2014 Lecture Notes in Computer Science  
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
more » ... t, which is proved by simulating a Turing machine by a cellular automaton with feedback. The same construction proves the Σ 0 2 -completeness of the finiteness problem for these grammars and automata.
doi:10.1007/978-3-642-54423-1_17 fatcat:e63ob2llvrdh5dx5uf7yhenpyu