The Power of Commuting with Finite Sets of Words

We construct a finite language L such that the largest language commuting with L is not recursively enumerable. This gives a negative answer to the question raised by Conway in 1971 and also strongly disproves Conway’s conjecture on context-freeness of maximal solutions of systems of semi-linear inequalities.

• Type: Journal
• Year: 2007
• Where: MST
• Authors: Michal Kunc
• Keywords: Largest Language, MST 2007, Negative Answer, finite Language