Optimal representation in average using Kolmogorov complexity

• Published in: Theoretical computer science Vol. 200; no. 1; pp. 261 - 287
• Main Authors: Rivals, E., Delahaye, J.P.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 28.06.1998; Elsevier
• Subjects: Algorithmics. Computability. Computer arithmetics; Applied sciences; Automata. Abstract machines. Turing machines; Compression; Computer science; control theory; systems; Data processing. List processing. Character string processing; Exact sciences and technology; Information theory; Kolmogorov complexity; Memory organisation. Data processing; Optimal coding; Software; Theoretical computing; Compression; Optimal coding; Kolmogorov complexity; Information theory; Logical function; Coding; Data compression; Kolmogorov law; Turing machine; Algorithmics; Data processing; Computational complexity
• ISSN: 0304-3975; 1879-2294
• DOI: 10.1016/S0304-3975(97)00275-2

One knows from the Algorithmic Complexity Theory 1 1 This theory is also called the Kolmogorov complexity or Algorithmic Information theory. [2–5, 8, 14] that a word is incompressible on average. For words of pattern x m , it is natural to believe that providing x and m is an optimal average representation. On the contrary, for words like x ⊕ y (i.e., the bit to bit x or between x and y), providing x and y is not an optimal description on average. In this work, we sketch a theory of average optimal representation that formalizes natural ideas and operates where intuition does not suffice. First, we formulate a definition of K-optimality on average for a pattern, then demonstrate results that corroborate intuitive ideas, and give worthy insights into the best compression in more complex cases.