Gregory J. Chaitin
- 1 HARDY, G. H., AND WRIGHT, E.M. An Introduction to the Theory of Numbers. Clarendon Press, Oxford, 1962.Google Scholar
- 2 DANTZIG, T. Number, the Language of Science. Macmillan, New York, 1954.Google Scholar
- 3 DAvis, M. Computability and Unsolvability. McGraw-Hill, New York, 1958.Google Scholar
- 4 GELFOND, A. O., AND LINmK, Yu. V. Elementary Methods in Analytic Number Theory. Rand McNally, Chicago, 1965.Google Scholar
- 5 BLUM, M. Measures on the computation speed of partial recursive functions. Quart. Prog. Rep. 72, Res. Lab. Electronics, MIT, Cambridge, Mass., Jan. 1964, pp. 237-253.Google Scholar
- 6 ARBIB, M. A. Speed-up theorems and incompleteness theorems. In Automata Theory, E. R. Cainiello (Ed.), Academic Press, New York, 1966, pp. 6-24.Google Scholar
- 7 FRAENKEL, A. A. Abstract Set Theory. North-Holland, Amsterdam, The Netherlands, 1961.Google Scholar
- 8 BOREL, R. Lemons sur la Th.orie des Fonctions. Gauthier-Villars, Paris, 1914.Google Scholar
- 9 HARDY, G. H. Orders of Infinity. Cambridge Math. Tracts, No. 12, U. of Cambridge, Cambridge, Eng., 1924.Google Scholar
- 10 Dekker, J. C. E., AND MYIILL, J. Retraceable sets. Canadian J. Math. 10 (1958), 357-373.Google Scholar
- 11 SOLOMONOFF, R.J. A formal theory of inductive inference, Pt. I. Inform. Contr. 7 (1964), 1-22.Google Scholar
- 12 KOLMOGOROV, A.N. Three approaches to the definition of the concept "amount of information." Problemy Peredachi Informatsii I (1965), 3-11. (Russian)Google Scholar
- 13 CHAITIN, G.J. On the length of programs for computing finite binary sequences: statistical considerations. J. ACM 16, 1 (Jam 1969), 145-159. Google Scholar
- 14 ARBIR, M. A., AND BLUM, M. Machine dependence of degrees of difficulty. Proc. Amer. Math. Soc. 16 (1965), 442-447.Google Scholar
- 15 BIRKHOFF, G. Lattice Theory. Amer. Math. Soc. Colloq. Publ. Vol. 25, Amer. Math. Soc., Providence, R. I., 1967.Google Scholar
- 16 CHAITIN, G.J. On the length of programs for computing ill, ire binary sequences. J. ACM 18, 4 (Oct. 1966), 547-569. Google Scholar
- 17 SACKS, G. E. Degrees of Unsolvability. No. 55, Annals of Math. Studies, Princeton U. Press, Princeton, N. J., 1963.Google Scholar
- 18 HARTMANIS, J., AND STEARNS, R.E. On the computational complexity of algorithms. Trans. Amer. Math. Soc. 117 (1965), 285-306.Google Scholar
- 19 BLUM, M. A machine-independent theory of the complexity of recursive functions. J. ACM 14, 2 (Apr. 1967), 322-336. Google Scholar
- 20 CHAITIN, G.J. A lattice of computer speeds. Abstract 67T-397, Notices Amer. Math. Soc. 14 (1967), 538.Google Scholar
- 21 MOSTOWSKI, A. ber gewisse universelle Relationen. Ann. Soc. Polon. Math. 17 (1938), 117-118.Google Scholar
- 22 BLUM, M. Oil the size of machines. Inform. Contr. 11 (1967), 257-265.Google Scholar
- 23 CHAITIN, G.J. On the difficulty of computations. Panamerican Symp. of Appl. Math., Buenos Aires, Argentina, Aug. 10, 1968. (to be published)Google Scholar
Index Terms
- On the Simplicity and Speed of Programs for Computing Infinite Sets of Natural Numbers
Recommendations
Monoidal intervals of clones on infinite sets
Let X be an infinite set of cardinality @k. We show that if L is an algebraic and dually algebraic distributive lattice with at most 2^@k completely join irreducibles, then there exists a monoidal interval in the clone lattice on X which is isomorphic ...
Axiomatizing rational power series over natural numbers
Iteration semi-rings are Conway semi-rings satisfying Conway's group identities. We show that the semi-rings N^r^a^t<<@S^*>> of rational power series with coefficients in the semi-ring N of natural numbers are the free partial iteration semi-rings. ...
Some mathematical structures of generalized rough sets in infinite universes of discourse
Transactions on rough sets XIIIThis paper presents a general framework for the study of mathematical structure of rough sets in infinite universes of discourse. Lower and upper approximations of a crisp set with respect to an infinite approximation space are first defined. Properties ...
Comments