论文信息 - A constructive generalization of the borel-cantelli lemma with application to the complexity of infinite strings

A constructive generalization of the borel-cantelli lemma with application to the complexity of infinite strings

This paper concerns a constructive adaptation of the classical Borel-Cantelli lemma which allows us to solve such decomposition problems as: when does there exist an infinite object that is decomposable into infinitely many parts that are maximally complex? A constructive proof is supplied of the key theorem and its degree is characterized. For completeness a classical (i.e., nonconstructive) proof is also provided.

Richard J. Lipton | Richard A. DeMillo | R. Lipton | R. DeMillo

[1] John Lamperti,et al. Wiener's test and Markov chains , 1963 .

[2] Volker Strassen,et al. Polynomials with Rational Coefficients Which are Hard to Compute , 1974, SIAM J. Comput..

[3] J. Spencer. Probabilistic Methods in Combinatorics , 1974 .

[4] Jr. Hartley Rogers. Theory of Recursive Functions and Effective Computability , 1969 .

[5] K. Chung,et al. On the application of the borel-cantelli lemma , 1952 .

[6] Richard J. Lipton. Polynomials with 0-1 coefficients that are hard to evaluate , 1975, 16th Annual Symposium on Foundations of Computer Science (sfcs 1975).

[7] A. Kolmogorov. Three approaches to the quantitative definition of information , 1968 .