Abstract
There are introduced and discussed stochastic and randomized P systems. Stochastic P systems are aimed to describe distortions which ay appear in evolution processes of membrane systems considered in the area of membrane computing. Randomized P systems serve for implementation of randomized algorithms. There is presented a family of randomized P systems which serve for implementation of Miller-Rabin randomized algorithm for primality of integers. P systems of this family verify primality of integers in a polynomial time,with a low error probability,and with a subexponential nu ber of processors modelled as membranes with evolving contents.
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References
E. Bach and J. Schallit,Algorithmic Number Theory, Cambridge, Massachusetts 1996.
G. Chiola, C. Dutheillet, G. Franceschinis,and S. Haddad, Stochastic well-formed coloured nets for symmetric modeling applications, IEEE Transactions on Computers Vol.42, No.11 (1993), pp.1343–1360.
P.J. Goss and J. Peccoud, Quantitative modelling of stochastic systems in molecular biology by using stochastic Petri nets, Proc.Nat.Acad.Sci.USA Vol.95, June 1998, pp.6750–6755.
N. Koblitz, Algebraic Aspects of Cryptography, Berlin 1998.
A.K. Lenstra, H.W.Jr. Lenstra, The Development of the Number Field Sieve, Lecture Notes in Mathematics Vol.1554, Berlin 1993.
M.A. Marsan, Stochastic Petri Nets:An Elementary Introduction, in Advances in Petri Nets 1989, ed.G. Rozenberg, Lecture Notes in Computer Science Vol.424, Berlin 1990, pp.1–29.
A. Obtu lowicz, Deterministic P systems for Solving SAT-problem, Romanian Journal of Information Science and Technology Vol.4, No.1–2, pp.195–201.
A. Obtu lowicz, On P systems with Active Membranes Solving the Integer Factorization Problem in a Polynomial Time, in Multiset Processing, ed.C.S. Calude et al., Lecture Notes in Computer Science Vol. 2235, Berlin 2001, pp.267–285.
Ch.H. Papadimitriou, Computational Complexity, Reading Massachusetts 1994.
G. Păun, P systems with Active Membranes: Attacking NP Complete Problems, Journal of Automata,Languages and Combinatorics 6 (2000), pp.75–90.
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Obtułowicz, A. (2003). Probabilistic P Systems. In: PĂun, G., Rozenberg, G., Salomaa, A., Zandron, C. (eds) Membrane Computing. WMC 2002. Lecture Notes in Computer Science, vol 2597. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36490-0_26
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DOI: https://doi.org/10.1007/3-540-36490-0_26
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