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CSR
2007
Springer

Conjunctive Grammars over a Unary Alphabet: Undecidability and Unbounded Growth

11 years 11 months ago
Conjunctive Grammars over a Unary Alphabet: Undecidability and Unbounded Growth
Abstract It has recently been proved (Je˙z, DLT 2007) that conjunctive grammars (that is, context-free grammars augmented by conjunction) generate some nonregular languages over a one-letter alphabet. The present paper improves this result by constructing conjunctive grammars for a larger class of unary languages. The results imply undecidability of a number of decision problems of unary conjunctive grammars, as well as nonexistence of an r.e. bound on the growth rate of generated languages. An essential step of the argument is a simulation of a cellular automaton recognizing positional notation of numbers using language equations.
Artur Jez, Alexander Okhotin
Added 07 Jun 2010
Updated 07 Jun 2010
Type Conference
Year 2007
Where CSR
Authors Artur Jez, Alexander Okhotin
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