Bennett, C. H, Gàcs, P., Li, M., Vitányi, M. B. and Zurek, W. H. (1998) Information distance. IEEE Transactions on Information Theory 44 1407–1423.

Calude, C. S. (2002) Information and Randomness: An Algorithmic Perspective, Springer-Verlag.

Calude, C. S. and Stay, M. A. (2006) Most programs stop quickly or never halt. Advances in Applied Mathematics 40 295–308.

Calude, C. S. and Stay, M. A. (2006) Natural halting probabilities, partial randomness, and zeta functions. Information and Computation 204 1718–1739.

Calude, C. S., Staiger, L. and Terwijn, S. A. (2006) On partial randomness. Annals of Pure and Applied Logic 138 20–30.

Chaitin, G. (1975) A theory of program size formally identical to information theory. Journal of the ACM 22 329–340.

Chaitin, G. (1976) Algorithmic entropy of sets. Computers and Mathematics with Applications 2 233–245.

Roberts, C. P. (2001) The Bayesian Choice: From Decision-Theoretic Foundations to Computational Implementation, Springer-Verlag.

Fredkin, E. and Toffoli, T. (1982) Conservative logic. International Journal of Theoretical Physics 21 219–253.

Janyes, E. T. (1957) Information theory and statistical mechanics. Physical Review 106 620–630.

Janyes, E. T. (2003) Probability Theory: The Logic of Science, Cambridge University Press.

Kolmogorov, A. N. (1965) Three approaches to the definition of the quantity of information. Problems of Information Transmission 1 3–11.

Kullback, S. and Leibler, R. A. (1951) On information and sufficiency. Annals of Mathematical Statistics 22 79–86.

Levin, L. A. (1973) Universal sequential search problems. Problems of Information Transmission 9 265–266.

Levin, L. A. (1974) Laws of information conservation (non-growth) and aspects of the foundation of probability theory. Problems of Information Transmission 10 206–210.

Levin, L. A. and Zvonkin, A. K. (1970) The complexity of finite objects and the development of the concepts of information and randomness by means of the theory of algorithms. Russian Mathematics Surveys 256 83–124.

Li, M. and Vitányi, P. (2008) An Introduction to Kolmogorov Complexity Theory and its Applications, Springer-Verlag.

Manin, Y. (2011) Renormalization and computation I: Motivation and background. In: Loday, J.-L. and Vallette, B. (eds.) OPERADS 2009. Séminaires et Congrès **26**, Société Mathématique de France 181–233.

Manin, Y. (2009) Renormalisation and computation II: time cut-off and the halting problem. *Mathematical Structures in Computer Science* (this issue).

Manin, Y. and Marcolli, M. (2009) Error-correcting codes and phase transitions. (Available as arXiv:0910.5135.)

Pour-El, M. B. and Richards, J. I. (1989) Computability in Analysis and Physics, Springer Verlag.

Reif, F. (1965) Fundamentals of Statistical and Thermal Physics, McGraw-Hill.

Rényi, A. (1960) On measures of information and entropy. In: Neyman, J. (ed.) Proceedings of the 4th Berkeley Symposium on Mathematical Statistics and Probability 1 547–561.

Solomonoff, R. J. (1964) A formal theory of inductive inference, part I. Information and Control 7 1–22.

Stoddard, E. J. (1919) Apparatus for obtaining power from compressed air, US Patent 1,926,463.

Szilard, L. (1929) On the decrease of entropy in a thermodynamic system by the intervention of intelligent beings. Zeitschrift für Physik 53 840–856. (English translation (2003) In: Leff, H. S. and Rex, A. F. (eds.) *Maxwell's Demon 2: Entropy, Information, Computing*, Adam Hilger.)

Tadaki, K. (2002) A generalization of Chaitin's halting probability Ω and halting self-similar sets. Hokkaido Mathematical Journal 31 219–253.

Tadaki, K. (2008) A statistical mechanical interpretation of algorithmic information theory. In: Local Proceedings of Computability in Europe 2008, University of Athens, Greece 425–434. (Available as arXiv:0801.4194.)

Tadaki, K. (2009) A statistical mechanical interpretation of algorithmic information theory III: Composite systems and fixed points. (Available as arXiv:0904.0973.)