Kraft-Chaitin Inequality Revisited

Kraft's inequality [9] is essential for the classical theory of noiseless coding [1, 8]. In algorithmic information theory [5, 7, 2] one needs an extension of Kraft's condition from finite sets to (infinite) recursively enumerable sets. This extension, known as Kraft-Chaitin Theorem, was obtained by Chaitin in his seminal paper [4] (see also, [3, 2]). The aim of this note is to offer a simpler proof of Kraft-Chaitin Theorem based on a new construction of the prefix-free code. 1.) C. Calude (ed.). The Finite, the Unbounded and the Infinite, Proceedings of the Summer School "Chaitin Complexity and Applications", Mangalia, Romania, 27 June - 6 July, 1995. 2.) The work of the first author has been partially supported by Auckland University Research Grant A18/ XXXXX/62090/3414050.