New applications of the incompressibility method: Part II

Abstract The incompressibility method is an elementary yet powerful proof technique. It has been used successfully in many areas (Li and Vitanyi, An Introduction to Kolmogorov Complexity and its Applications, Springer, New york, 1997). To further demonstrate its power and elegance we exhibit new simple proofs using the incompressibility method.

[1]  Roman Bek,et al.  Discourse on one way in which a quantum-mechanics language on the classical logical base can be built up , 1978, Kybernetika.

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

[3]  Osamu Watanabe,et al.  Orientation Selectivity: An Approach from Theoretical Computer Science , 1996 .

[4]  Gonzalo Navarro,et al.  Bounding the Expected Length of Longest Common Subsequences and Forests , 1999, Theory of Computing Systems.

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

[6]  Mike Paterson,et al.  Longest Common Subsequences , 1994, MFCS.

[7]  Joseph G. Deken Some limit results for longest common subsequences , 1979, Discret. Math..

[8]  Ming Li,et al.  An Introduction to Kolmogorov Complexity and Its Applications , 2019, Texts in Computer Science.

[9]  David Sankoff,et al.  Time Warps, String Edits, and Macromolecules: The Theory and Practice of Sequence Comparison , 1983 .

[10]  Don Coppersmith,et al.  Matrix multiplication via arithmetic progressions , 1987, STOC.

[11]  V. Chvátal,et al.  Longest common subsequences of two random sequences , 1975, Advances in Applied Probability.

[12]  Mike Paterson,et al.  Upper Bounds for the Expected Length of a Longest Common Subsequence of Two Binary Sequences , 1994, Random Struct. Algorithms.

[13]  Patrick E. O'Neil,et al.  A Fast Expected Time Algorithm for Boolean Matrix Multiplication and Transitive Closure , 1973, Inf. Control..

[14]  Ming Li,et al.  Kolmogorov Complexity Arguments in Combinatorics , 1994, J. Comb. Theory, Ser. A.

[15]  Gerald L. Alexanderson,et al.  The William Lowell Putnam mathematical competition , 1986 .

[16]  G. J. Chaitin A note on the number of N -bit strings with maximum complexity , 1993 .

[17]  W. Feller,et al.  An Introduction to Probability Theory and Its Applications. Vol. 1, Second Edition. , 1958 .

[18]  RAVI VAKIL,et al.  THE WILLIAM LOWELL PUTNAM MATHEMATICAL COMPETITION. , 1942, Science.

[19]  Michael Werman,et al.  On computing majority by comparisons , 1991, Comb..

[20]  Rolf Niedermeier,et al.  Towards optimal locality in mesh-indexings , 1997, Discret. Appl. Math..

[21]  Noga Alon,et al.  The Probabilistic Method , 2015, Fundamentals of Ramsey Theory.

[22]  René Schott,et al.  The Average-Case Complexity of Determining the Majority , 1997, SIAM J. Comput..

[23]  Edward M. Reingold,et al.  Determining the Majority , 1993, Inf. Process. Lett..

[24]  Tao Jiang,et al.  New Applications of the Incompressibility Method , 1999, Comput. J..

[25]  Eyal Kushilevitz,et al.  Communication Complexity , 1997, Adv. Comput..

[26]  Tao Jiang,et al.  On the Approximation of Shortest Common Supersequences and Longest Common Subsequences , 1994, SIAM J. Comput..

[27]  Shane S. Sturrock,et al.  Time Warps, String Edits, and Macromolecules – The Theory and Practice of Sequence Comparison . David Sankoff and Joseph Kruskal. ISBN 1-57586-217-4. Price £13.95 (US$22·95). , 2000 .

[28]  Pál Révész,et al.  Random walk in random and non-random environments , 1990 .

[29]  Feller William,et al.  An Introduction To Probability Theory And Its Applications , 1950 .

[30]  Tao Jiang,et al.  On the Approximation of Shortest Common Supersequences and Longest Common Subsequences , 1995, SIAM J. Comput..

[31]  Mike Paterson,et al.  Upper Bounds for the Expected Length of a Longest Common Subsequence of Two Binary Sequences , 1995, Random Struct. Algorithms.

[32]  D. Knuth,et al.  Mathematics for the Analysis of Algorithms , 1999 .

[33]  阿部 浩一,et al.  Fundamenta Mathematicae私抄 : 退任の辞に代えて , 1987 .

[34]  Leonard F. Klosinski,et al.  The William Lowell Putnam mathematical competition: problems and solutions: 1965-1984 , 1985 .