Coincidental extension of scattered context languages

Abstract.

For a symbol, #, and a string, x = a ₁ a ₂ ...a _{n - 1} a _n , any string of the form # ⁱ a ₁ # ⁱ a ₂ # ⁱ...# ⁱ a _{n - 1} # ⁱ a _n # ⁱ, where 0, is a coincidental #-extension of x. A language, K, is a coincidental #-extension of L if every string of K represents a coincidental extension of a string in L and the deletion of all #s in K results in L. This paper proves that for every recursively enumerable language, E, there exists a propagating scattered context language that represents a coincidental extension of E.