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.

• Type: Conference
• Year: 2007
• Where: CSR
• Authors: Artur Jez, Alexander Okhotin
• Keywords: Conjunctive Grammars, Context-free Grammars, CSR 2007, Unary Conjunctive Grammars