Abstract
A time-varying distributed H system (TVDH system) is a splicing system which has the following feature: at different moments one uses different sets of splicing rules (these sets are called components of TVDH system). The number of components is called the degree of the TVDH system. The passing from a component to another one is specified in a cycle. It was proved by both authors (1999) that TVDH systems of degree 2 generate all recursively enumerable languages. It was made by modelling Turing machines and, in that modelling, every language is generated “step by step” or “word by word”. This solution is not a fully parallel one. A.Paun (1999) presented a complete parallel solution for TVDH systems of degree 4 by modelling type 0 formal grammars. Now we improved A.Paun’s result by reducing the number of components of such TVDH systems down to 3. This question is open for 2 components, i.e. is it possible to construct TVDH systems of degree 2 which completely uses the parallel nature of molecular computations based on splicing operations (say model type 0 formal grammars)?
We consider also original G.Paun’s definition of TVDH systems and suggest a slightly different definition of TVDH systems based on the definition of H systems — extended time-varying distributed H systems (ETVDH systems). For this new definition we proved that ETVDH systems with one component generate exactly the set of all regular languages and that with two components, they generate exactly the set of all recursively enumerable languages.
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
Csuhaj-Varjù, E., Kari, L., Păun, G.: Test Tube distributed system based on splicing. Computer and AI. 2-3 (1996) 211–232
Ferretti, C., Mauri, G., Zandron, C.: Nine test tubes generate any RE language. TCS. 231, no.2 (2000) 171–180
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, A. Salomaa, eds., Handbook of Formal Languages, 3 volumes, Springer-Verlag, Heidelberg (1997)
Margenstern, M.: Frontier between decidability and undecidability: a survey. TCS. 231, no.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. Publications du GIFM, no. 99-102, I.U.T., Metz (France), ISBN 2-9511539-5-3 (1999)
Păun, A.: On Time-Varying H Systems. Bulletin of EATCS. 67 (1999) 157–164
Păun, G.: Regular extended H systems are computationally universal. Journal of Automata, Languages and Combinatorics 1, no.1 (1996) 27–36
Păun, G., Rozenberg, G., Salomaa, A.: Computing by splicing. TCS. 168, no.2 (1996) 321–336
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, no.2 (2000) 275–296
Păun, G., Rozenberg, G., Salomaa, A.: DNA Computing: New Computing Paradigms. Springer, Heidelberg (1998)
Pixton, D.: Regularity of splicing languages. Descrete Applied Mathematics 69 (1996) 101–124
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, T.E. Klein, eds), World Sci. Publ., Singapure (1998) 545–556
Rogozhin, Yu.: Small universal Turing machines. TCS. 168, no.2 (1996) 215–240
Rogozhin, Yu.: A Universal Turing Machine with 22 States and 2 Symbols. Romanian Journal of Information Science and Technology 1, no.3 (1998) 259–265
Verlan, S.: On extended time-varying distributed H systems. Poster at DNA6 conference, Leiden (2000)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Margenstern, M., Rogozhin, Y. (2001). About time-varying distributed H systems. In: Condon, A., Rozenberg, G. (eds) DNA Computing. DNA 2000. Lecture Notes in Computer Science, vol 2054. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44992-2_5
Download citation
DOI: https://doi.org/10.1007/3-540-44992-2_5
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-42076-7
Online ISBN: 978-3-540-44992-8
eBook Packages: Springer Book Archive