T - Complexity and T - Information Theory – an Executive Summary , 2 nd revised version

This paper describes the derivation of the T-complexity and T-information theory from the decomposition of finite strings, based on the duality of strings and variable-length T-codes. It further outlines its similarity to the string parsing algorithm by Lempel and Ziv. In its first version [15], it was intended as a summary of work published mainly by Titchener and Nicolescu. Apart from minor corrections, the present extended version incorporates feedback from previous readers and presents new results obtained since. 1 A brief introduction to T-codes This paper first gives an introduction to T-codes and their construction technique, as this is fundamental for the understanding of the T-decomposition algorithm that underpins the T-complexity measure. It also assists in its physical interpretation. T-codes [3, 4, 11] are similar to Huffman codes in that they are codes with variable-length codewords. Depending on the source symbol probabilities, a Huffman code may also be a T-code. In fact, any T-code set could theoretically have been constructed as a result of a Huffman code construction algorithm. By inference, every T-code set is complete, a property also called exhaustive by some authors. In complete codes, all internal nodes of the (Huffman) decoding tree are fully populated. Moreover, like Huffman codes, T-codes are prefix codes, again a property that is also – somewhat confusingly – known as prefix-freeness, implying that no codeword in the set is a proper prefix of another. Similarities largely end there, however. Most Huffman codes are not Tcodes, and at least from today’s perspective, the significance of T-codes is not in Huffman-like source coding. Rather than letting the source symbol probabilities determine the length of the codewords and the structure of the decoding