MFCS '01 Proceedings of the 26th International Symposium on Mathematical Foundations of Computer Science
Randomness, Computability, and Density
STACS '01 Proceedings of the 18th Annual Symposium on Theoretical Aspects of Computer Science
The dimensions of individual strings and sequences
Information and Computation
Journal of Computer and System Sciences
CATS '09 Proceedings of the Fifteenth Australasian Symposium on Computing: The Australasian Theory - Volume 94
TAMC'11 Proceedings of the 8th annual conference on Theory and applications of models of computation
Arithmetic complexity via effective names for random sequences
ACM Transactions on Computational Logic (TOCL)
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We obtain some dramatic results using statistical mechanics-thermodynamics kinds of arguments concerning randomness, chaos, unpredictability, and uncertainty in mathematics. We construct an equation involving only whole numbers and addition, multiplication, and exponentiation, with the property that if one varies a parameter and asks whether the number of solutions is finite or infinite, the answer to this question is indistinguishable from the result of independent tosses of a fair coin. This yields a number of powerful Godel incompleteness-type results concerning the limitations of the axiomatic method, in which entropy-information measures are used.