Review of Feasible Computations and Provable Complexity Properties by Juris Hartmanis
Abstract
"It may only be a slight exaggeration to claim that in the 1930s we started to understand what is and is not effectively computable and that in the 1970s we started to understand what is and is not practically or feasibly computable. There is no doubt that the results about what can and cannot be effectively computed or formalized in mathematics have had a profound influence on mathematics, and, even more broadly, they have influenced our view of our scientific methods. We believe that the results about what can and cannot be practically computed will also have a major influence on computer science, mathematics, and even though more slowly, will affect other research areas and influence how we think about scientific theories." - Juris Hartmanis (from the Introduction)
References
[1]
[Aa] S. AARONSON, "Is P versus NP formally independent?" in Bulletin of the EATCS 81, pp. 109--136 (2003). Also http://people.cs.uchicago.edu/?fortnow/beatcs/column81.pdf. [BGS] T. P. BAKER, J. GILL, AND R. SOLOVAY, "Relativizations of the P=?NP question," in SIAM Journal on Computing, 4(4), pp. 431--442 (1975).
[2]
[BH] L. BERMAN AND J. HARTMANIS, On isomorphisms and density of NP and other complete sets, inSIAM Journal on Computing, 6(2), pp. 305--322 (1977).
[3]
[CO] J.-Y. CAI AND M. OGIHARA, "Sparse Sets versus Complexity Classes," in Complexity Theory Retrospective II, Lane A. Hemaspaandra and Alan L. Selman, eds., Springer 1997, pp. 53--80.]
[4]
[Ha] J. HARTMANIS, "Computational complexity of one-tape Turing machine computations," in Journal of the ACM, 15, pp. 339--352 (1968).
[5]
[KL] R. KARP AND R. LIPTON, "Turing machines that take advice," in L'enseignement Math´ematique, 28(3/4), pp. 191--209 (1982).
[6]
[Ma] S. MAHANEY, "Sparse complete sets for NP: Solution of a conjecture of Berman and Hartmanis," Journal of Computer and System Sciences, 25(2) pp. 130--143 (1982).
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Association for Computing Machinery
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Publication History
Published: 19 December 2022
Published in SIGACT Volume 53, Issue 4
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