Abstract
We introduce a new variant of the heavily studied model of H systems. The new variant will use an external factor to determine the set of the active splicing rules. We improve the best known universality result for time-varying H systems with respect to the diameter of such a system and we prove that if the function recording the behavior of the external factor is uncomputable so is the newly defined model, thus exceeding the Turing barrier. We also construct an universal system that is also more powerful than the Turing Machines.
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References
Calude, C.S., Păun, G.: Bio-Steps Beyond Turing. CDMTCS Tech. Rep. No. 226, 1–28 (2003)
Chaitin, G.J.: Information, Randomness and Incompleteness, Papers on Algorithmic Information Theory. World Scientific, Singapore (1987) (2nd ed., 1990)
Copeland, B.J.: Hypercomputation. Minds and Machines 12(4), 461–502 (2002)
Delahaye, J.-P.: La barrière de Turing. Pour la Science 312, 90–95 (2003)
Hopcroft, J.E., Ullman, J.D.: Introduction to Automata Theory, Languages, and Computation. Addison-Wesley, Reading (1979)
Head, T.: Formal language theory and DNA: an analysis of the generative capacity of specific recombinant behaviors. Bull. Math. Biology 49, 737–759 (1987)
Margenstern, M., Rogozhin, Y.: Time-Varying Distributed H Systems of Degree 1 Generate All Recursively Enumerable Languages. In: Proc. of Workshop on Membrane Computing (WMC-CdeA 2001), Curtea-de-Argeş, România, pp. 199–207 (2001)
Margenstern, M., Rogozhin, Y.: A Universal Time-Varying Distributed H System of Degree 1. In: Jonoska, N., Seeman, N.C. (eds.) DNA 2001. LNCS, vol. 2340, pp. 371–380. Springer, Heidelberg (2002)
Margenstern, M., Rogozhin, Y.: An universal time-varying distributed H system of degree 2. In: Preliminary Proc. of Fourth Intern. Meeting on DNA Based Computers, pp. 83–84. Pennsylvania Univ. (June 1998)
Margenstern, M., Rogozhin, Y., Verlan, S.: Time-Varying Distributed H Systems with Parallel Computations: The Problem Is Solved. In: Goss, G., Hartmanis, J., van Leeuwen, J. (eds.) DNA 2003. LNCS, vol. 2943, pp. 48–53. springer, Berlin (2004)
Păun, A.: On Time-varying H Systems. Bulletin of the EATCS 67, 157–164 (1999)
Păun, A.: On controlled extended H systems of small radius. Fundamenta Informaticae 31(2), 185–193 (1997)
Păun, G., Rozenberg, G., Salomaa, A.: DNA Computing. New Computing Paradigms. Springer, Heidelberg (1998)
Rozenberg, G., Salomaa, A. (eds.): Handbook of Formal Languages. Springer, Heidelberg (1997)
Teuscher, C., Sipper, M.: Hypercomputation: Hyper or computation? Communications ACM 45(8), 23–24 (2002)
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Câmpeanu, C., Păun, A. (2005). Computing Beyond the Turing Limit Using the H Systems. In: Ferretti, C., Mauri, G., Zandron, C. (eds) DNA Computing. DNA 2004. Lecture Notes in Computer Science, vol 3384. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11493785_3
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DOI: https://doi.org/10.1007/11493785_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-26174-2
Online ISBN: 978-3-540-31844-6
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