Abstract
Time-varying distributed H systems (TVDH systems shortly) of degree n are a well known model of splicing computations which has the following special feature: at different moments one uses different sets of splicing rules (the number of these sets of splicing rules is called the degree of the TVDH system). It is known that there is a universal TVDH system of degree 2. Now we prove that there is a universal TVDH system of degree 1. It is a surprising result because we did not thought that these systems are so powerful.
Recently both authors proved that TVDH systems of degree 1 can generate any recursively enumerable languages. We present here the short description of the main idea of the proof that result.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Head, T.: Formal language theory and DNA: an analysis of the generative capacity of recombinant behaviors. Bulletin of Mathematical Biology 49 (1987), 737–759.
Head, T., Păun, Gh., Pixton, D.: Language theory and molecular genetics. Generative mechanisms suggested by DNA recombination. Chapter 7 in vol. 2 of G. Rozenberg and A. Salomaa, eds., Handbook of Formal Languages, 3 volumes, Springer-Verlag, Heidelberg, 1997.
Kleene, S.: Introduction to Metamathematics. Van Nostrand Comp. Inc., New-York, 1952.
Margenstern, M.: Non-erasing Turing machines: a new frontier between a decidable halting problem and universality. Lecture Notes in Computer Science 911, in Proceedings of LATIN’95 (1995), 386–397.
Margenstern, M.: Frontier between decidability and undecidability: a survey. TCS 231-2 (2000), 217–251.
Margenstern, M., Rogozhin, Yu.: A universal time-varying distributed H-system of degree 2. In Preliminary proceedings, Fourth International Meeting on DNA Based Computers, June 15–19, 1998, University of Pennsylvania (1998), 83–84.
Margenstern, M., Rogozhin, Yu.: A universal time-varying distributed H-system of degree 2. Biosystems, 52 (1999), 73–80.
Margenstern, M., Rogozhin, Yu.: Generating all recursively enumerable languages with a time-varying distributed H-system of degree 2, Technical Report in Publications du G.I.F.M., Institut Universitaire de Technologie de Metz, ISBN 2-9511539-5-3, 1999.
Margenstern, M., Rogozhin, Yu.: About Time-Varying Distributed H systems. In Proceedings of DNA Based Computers Conference, 6, Leiden, The Netherlands (2000), 55–64.
Margenstern, M., Rogozhin, Yu.: About Time-Varying Distributed H systems. DNA Computing, 6th International Workshop on DNA-Based Computers, DNA 2000, Leiden, The Netherlands, June 13–17, 2000, LNCS 2054 (2001), 53–62.
Margenstern, M., Rogozhin, Yu.: Time-Varying Distributed H-systems of Degree 2 Generate All Recursively Enumerable Languages. Where Mathematics, Computer Science, Linguistics and Biology Meet. Kluwer Academic Publishers (2001), 399–407.
Cocke, J., Minsky, M.: Universality of tag systems with P = 2. J. Assoc. Comput. Mach. 11 (1964), 15–20.
Minsky, M.L.: Computations: Finite and Infinite Machines. Prentice Hall, Engle-wood Cliffs, NJ, 1967
Priese, L.: Towards a precise characterization of the complexity of universal and nonuniversal Turing machines. SIAM Journal of Computation, 8,4 (1979) 508–523
Priese, L., Rogozhin, Yu., Margenstern, M.: Finite H-Systems with 3 Test Tubes are not Predictable. In Proceedings of Pacific Symposium on Biocomputing, Kapalua, Maui, January 1998, R.B. Altman, A.K. Dunker, L. Hunter, and T.E. Klein, (eds.), World Sci. Publ., Singapore (1998), 545–556.
Păun, A.: On Time-Varying H Systems. Bulletin of EATCS, No. 67, (February 1999), 157–164.
Păun, G.: DNA computing: distributed splicing systems. in Structures in Logic and Computer Science. A Selection of Essays in honor of A. Ehrenfeucht, LNCS 1261 (1997), 353–370.
Păun, G.: DNA Computing Based on Splicing: Universality Results. TCS 231-2 (2000), 275–296.
Păun, G., Rozenberg, G., Salomaa, A.: DNA Computing: New Computing Paradigms. Springer, 1998.
Rogozhin, Yu.: Seven universal Turing machines. Mathematical Studies, Kishinev, Academy of Sciences, 69 (1982), 76–90. (In Russian).
Rogozhin, Yu.: Small universal Turing machines. TCS 168-2 (1996) 215–240.
Rogozhin, Yu.: A Universal Turing Machine with 22 States and 2 symbols. Romanian Journal of Information Science and Technology, 1,3 (1998), 259–265.
Verlan, S.: On Extended Time-Varying Distributed H Systems. In Proceedings of DNA Based Computers Conference, 6, Leiden, The Netherlands (2000) 281.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Margenstern, M., Rogozhin, Y. (2002). A Universal Time-Varying Distributed H System of Degree 1. In: Jonoska, N., Seeman, N.C. (eds) DNA Computing. DNA 2001. Lecture Notes in Computer Science, vol 2340. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48017-X_35
Download citation
DOI: https://doi.org/10.1007/3-540-48017-X_35
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-43775-8
Online ISBN: 978-3-540-48017-4
eBook Packages: Springer Book Archive