Formularless Logic Function
Author(s)
Alexey Nikolayevitch Teterin
ABSTRACT
The concept of computability is defined more exactly and illustrated as an example of Boolean functions and cryptanalysis. To define a Boolean function is not necessary to record its formula. To do that the reduced (compact) description of values is determined in the truth table or in the statement of the problem. We obtain estimates of computation time, the volume of a compact descriptions and the range of variables under which it takes the value 0 or 1, depending polynomially on the number of arguments.
The concept of computability is defined more exactly and illustrated as an example of Boolean functions and cryptanalysis. To define a Boolean function is not necessary to record its formula. To do that the reduced (compact) description of values is determined in the truth table or in the statement of the problem. We obtain estimates of computation time, the volume of a compact descriptions and the range of variables under which it takes the value 0 or 1, depending polynomially on the number of arguments.
Cite this paper
A. Teterin, "Formularless Logic Function," Open Journal of Discrete Mathematics, Vol. 3 No. 1, 2013, pp. 21-24. doi: 10.4236/ojdm.2013.31005.
A. Teterin, "Formularless Logic Function," Open Journal of Discrete Mathematics, Vol. 3 No. 1, 2013, pp. 21-24. doi: 10.4236/ojdm.2013.31005.
References
[1] A. N. Teterin, “Classification on Bounded Sets,” Pattern Recognition and Image Analysis, Vol. 20, No. 4, 2010, pp. 564-572. doi:10.1134/S1054661810040188 [2] A. N. Teterin, “А Geometric Approach to Classification: New Model of the Operation of a Neuron,” Computational Mathematics and Mathematical Physics, Vol. 32, No. 12, 1992, pp. 1797-1805. [3] E. M. Gold, “Language Identification in the Limit,” Information and Control, Vol. 10, No. 5, 1967, pp. 447-474. doi:10.1016/S0019-9958(67)91165-5 [4] M. Burgin, A. Klinger, Experience, “Generations, and Limits in Machine Learning,” Theoretical Computer Science, Vol. 317, No. 1-3, 2004, pp. 71-91. doi:10.1016/j.tcs.2003.12.005 [5] P. Orponen, “A Survey of Continuous-Time Computation Theory,” In: D.-Z. Du and K.-I. Ko, Eds., Advances in Algorithms, Languages, and Complexity, Springer, Berlin, 1997, рp. 209-224. [6] C. Moore, “Recursion Theory on the Reals and Continuous-Time Computation,” Theoretical Computer Science, Vol. 162, No. 1, 1996, pp. 23-44. doi:10.1016/0304-3975(95)00248-0
[1] A. N. Teterin, “Classification on Bounded Sets,” Pattern Recognition and Image Analysis, Vol. 20, No. 4, 2010, pp. 564-572. doi:10.1134/S1054661810040188 [2] A. N. Teterin, “А Geometric Approach to Classification: New Model of the Operation of a Neuron,” Computational Mathematics and Mathematical Physics, Vol. 32, No. 12, 1992, pp. 1797-1805. [3] E. M. Gold, “Language Identification in the Limit,” Information and Control, Vol. 10, No. 5, 1967, pp. 447-474. doi:10.1016/S0019-9958(67)91165-5 [4] M. Burgin, A. Klinger, Experience, “Generations, and Limits in Machine Learning,” Theoretical Computer Science, Vol. 317, No. 1-3, 2004, pp. 71-91. doi:10.1016/j.tcs.2003.12.005 [5] P. Orponen, “A Survey of Continuous-Time Computation Theory,” In: D.-Z. Du and K.-I. Ko, Eds., Advances in Algorithms, Languages, and Complexity, Springer, Berlin, 1997, рp. 209-224. [6] C. Moore, “Recursion Theory on the Reals and Continuous-Time Computation,” Theoretical Computer Science, Vol. 162, No. 1, 1996, pp. 23-44. doi:10.1016/0304-3975(95)00248-0