Free-Extendible Prefix-Free Sets and an Extension of the Kraft-Chaitin Theorem

First, the dual set of a finite prefix-free set is defined. Using this notion we describe equivalent conditions for a finite prefix-free set to be indefinitely extendible. This lead to a simple proof for the Kraft-Chaitin Theorem. Finally, we discuss the influence of the alphabet size on the indefinite extensibility property. 1 C.S.Calude and G.Stefanescu (eds.). Automata, Logic, and Computability. Special issue dedicated to Professor Sergiu Rudeanu Festschrift.