On P Systems with Active Membranes Solving the Integer Factorization Problem in a Polynomial Time
There are presented deterministic P systems with active membranes which are able to solve the Integer Factorization Problem in a polynomial time, which is the main result of the paper. There is introduced a class of programs for the description and correct implementation of algorithms of elementary number theory in nonstandard computing systems, especially in P systems with active membranes. By using some of these programs there is achieved the main result.
Unable to display preview. Download preview PDF.
- Brainerd, W. S., Landweber, L. H. (1974): Theory of Computation. New YorkGoogle Scholar
- Koblitz, N. (1998): Algebraic Aspects of Cryptography. BerlinGoogle Scholar
- Lenstra, A. K., Lenstra, H. W., Jr. (1993): The Development of the Number Field Sieve. Lecture Notes in Mathematics, 1554, BerlinGoogle Scholar
- Menezes, A. J., van Oorschot, P. C., Vanstone, S. A. (1996): Handbook of Applied Cryptography. CRC Press, Boca RatonGoogle Scholar
- Meyer, A. R., Ritchie, D. M. (1967): The complexity of loop programs. Proceedings of the ACM National Meeting, ACM Pub. P-67, 465–469Google Scholar
- Papadimitriou, Ch. P. (1994): Computational Complexity. Reading, MassachusettsGoogle Scholar
- [2000a]Păun, Gh. (2000a): P-Systems with Active Membranes: Attacking NP Complete Problems. Journal of Automata, Languages and Combinatorics, 6 (2000), 75–90Google Scholar