Abstract
In this article we present an overview of the study of the universality problem in the area of molecular and cellular computing. We consider the results that deal explicitly with this problem and that aim to optimize the obtained construction. A particular attention is given to models based on the splicing operation as well as to multiset-rewriting based models.
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References
Alhazov, A., Kogler, M., Margenstern, M., Rogozhin, Y., Verlan, S.: Small universal TVDH and test tube systems. Int. J. Found. Comput. Sci. 22(1), 143–154 (2011)
Alhazov, A., Martín-Vide, C., Truthe, B., Dassow, J., Rogozhin, Y.: On networks of evolutionary processors with nodes of two types. Fundamenta Informaticae 91(1), 1–15 (2009)
Alhazov, A., Rogozhin, Y., Verlan, S.: On small universal splicing systems. Int. J. Found. Comput. Sci. 23(07), 1423–1438 (2012)
Alhazov, A., Verlan, S.: Minimization strategies for maximally parallel multiset rewriting systems. Theor. Comput. Sci. 412(17), 1581–1591 (2011)
Barzdin, I.M.: On a class of turing machines (Minsky machines). Algebra i Logika 1, 42–51 (1963). (in Russian)
Bonnet, R.: The reachability problem for vector addition system with one zero-test. In: Murlak, F., Sankowski, P. (eds.) MFCS 2011. LNCS, vol. 6907, pp. 145–157. Springer, Heidelberg (2011)
Castellanos, J., Martín-Vide, C., Mitrana, V., Sempere, J.M.: Solving NP-complete problems with networks of evolutionary processors. In: Mira, J., Prieto, A.G. (eds.) IWANN 2001. LNCS, vol. 2084, pp. 621–628. Springer, Heidelberg (2001)
Csuhaj-Varjú, E., Kari, L., Păun, G.: Test tube distributed systems based on splicing. Comput. Artif. Intell. 15(2–3), 211–232 (1996)
Dassow, J., Manea, F.: Accepting hybrid networks of evolutionary processors with special topologies and small communication. In: Proceedings of DCFS 2010, of EPTCS, vol. 31, pp. 68–77 (2010)
Dassow, J., Manea, F., Truthe, B.: On the power of accepting networks of evolutionary processors with special topologies and random context filters. Fundamenta Informaticae 136(1–2), 1–35 (2015)
Dassow, J., Mitrana, V.: Accepting networks of non-inserting evolutionary processors. In: Priami, C., Back, R.-J., Petre, I. (eds.) Transactions on Computational Systems Biology XI. LNCS, vol. 5750, pp. 187–199. Springer, Heidelberg (2009)
Demaine, E.D., Demaine, M.L., Fekete, S.P., Patitz, M.J., Schweller, R.T., Winslow, A., Woods, D.: One tile to rule them all: simulating any tile assembly system with a single universal tile. In: Esparza, J., Fraigniaud, P., Husfeldt, T., Koutsoupias, E. (eds.) ICALP 2014. LNCS, vol. 8572, pp. 368–379. Springer, Heidelberg (2014)
Doty, D., Lutz, J.H., Patitz, M.J., Schweller, R.T., Summers, S.M., Woods, D.: The tile assembly model is intrinsically universal. In: Proceedings of the 53rd Annual IEEE Symposium on Foundations of Computer Science, pp. 302–310 (2012)
Freund, R., Oswald, M.: A small universal antiport P system with forbidden context. In: Leung, H., Pighizzini, G. (eds.) 8th International Workshop on Descriptional Complexity of Formal Systems, pp. 259–266. Proceedings, New Mexico (2006)
Freund, R., Verlan, S.: A formal framework for static (Tissue) P systems. In: Eleftherakis, G., Kefalas, P., Păun, G., Rozenberg, G., Salomaa, A. (eds.) WMC 2007. LNCS, vol. 4860, pp. 271–284. Springer, Heidelberg (2007)
Frisco, P.: Direct constructions of universal extended H systems. Theor. Comput. Sci. 296(2), 269–293 (2003)
Frisco, P., Hoogeboom, H.J., Sant, P.: A direct construction of a universal P system. Fundamenta Informaticae 49(1–3), 103–122 (2002)
Head, T.: Formal language theory and DNA: an analysis of the generative capacity of specific recombinant behaviors. Bull. Math. Biol. 49(6), 737–759 (1987)
Head, T.: Splicing languages generated with one sided context. In: Paun, G. (ed.) Computing with Bio-Molecules. Theory and Experiments, pp. 158–181. Springer, Singapore (1998)
Hopcroft, J., Pansiot, J.-J.: On the reachability problem for 5-dimensional vector addition systems. Theor. Comput. Sci. 8(2), 135–159 (1979)
Ivanov, S., Pelz, E., Verlan, S.: Small universal Petri nets with inhibitor arcs (2013). arXiv, CoRR. abs/1312.4414
Ivanov, S., Pelz, E., Verlan, S.: Small universal non-deterministic Petri nets with inhibitor arcs. In: Jürgensen, H., Karhumäki, J., Okhotin, A. (eds.) DCFS 2014. LNCS, vol. 8614, pp. 186–197. Springer, Heidelberg (2014)
Ivanov, S., Rogozhin, Y., Verlan, S.: Small universal networks of evolutionary processors. J. Autom. Lang. Comb. 19(1—-4), 133–144 (2014)
Kari, L.: DNA computing: arrival of biological mathematics. Math. Intell. 19(2), 9–22 (1997)
Kim, J., White, K.S., Winfree, E.: Construction of an in vitro bistable circuit from synthetic transcriptional switches. Mol. Syst. Biol. 2, 68 (2006)
Korec, I.: Small universal register machines. Theor. Comput. Sci. 168(2), 267–301 (1996)
Krassovitskiy, A., Rogozhin, Y., Verlan, S.: Further results on insertion-deletion systems with one-sided contexts. In: Martín-Vide, C., Otto, F., Fernau, H. (eds.) LATA 2008. LNCS, vol. 5196, pp. 333–344. Springer, Heidelberg (2008)
Lathrop, J.I., Lutz, J.H., Patitz, M.J., Summers, S.M.: Computability and complexity in self-assembly. Theory Comput. Syst. 48(3), 617–647 (2011)
Loos, R., Manea, F., Mitrana, V.: On small, reduced, and fast universal accepting networks of splicing processors. Theor. Comp. Sci. 410(45), 406–416 (2009)
Malcev, A.I.: Algorithms and Recursive Functions. Wolters-Noordhoff, Groningen (1970)
Manea, F., Martín-Vide, C., Mitrana, V.: On the size complexity of universal accepting hybrid networks of evolutionary processors. Math. Struct. Comput. Sci. 8, 17:753–771 (2007)
Manea, F., Martín-Vide, C., Mitrana, V.: Accepting Networks of Evolutionary Word and Picture Processors: A Survey, pp. 525–561. Imperial College Press, London (2010). Chap. 10
Margenstern, M.: Frontier between decidability and undecidability: a survey. Theor. Comput. Sci. 231(2), 217–251 (2000)
Margenstern, M., Rogozhin, Y.: Time-varying distributed H systems of degree 1 generate all recursively enumerable languages. In: Ito, M., Păun, G., Yu, S. (eds.) Words, Semigroups, and Transductions, pp. 329–339. World Scientific, Singapore (2001)
Margenstern, M., Rogozhin, Y., Verlan, S.: Time-varying distributed H systems with parallel computations: the problem is solved. In: Chen, J., Reif, J.H. (eds.) DNA 2003. LNCS, vol. 2943, pp. 48–53. Springer, Heidelberg (2004)
Matveevici, A., Rogozhin, Y., Verlan, S.: Insertion-deletion systems with one-sided contexts. In: Durand-Lose, J., Margenstern, M. (eds.) MCU 2007. LNCS, vol. 4664, pp. 205–217. Springer, Heidelberg (2007)
Minsky, M.: Size and structure of universal Turing machines using tag systems. In: Recursive Function Theory: Proceedings, Symposium in Pure Mathematics, vo. 5, pp. 229–238. Provelence (1962)
Minsky, M.: Computations: Finite and Infinite Machines. Prentice Hall, USA (1967)
Neary, T., Woods, D.: The complexity of small universal turing machines: a survey. In: Bieliková, M., Friedrich, G., Gottlob, G., Katzenbeisser, S., Turán, G. (eds.) SOFSEM 2012. LNCS, vol. 7147, pp. 385–405. Springer, Heidelberg (2012)
Ollinger, N.: Automates cellulaires: structures. Ph.D. thesis, ENS Lyon (2002)
Ollinger, N.: The quest for small universal cellular automata. In: Widmayer, P., Triguero, F., Morales, R., Hennessy, M., Eidenbenz, S., Conejo, R. (eds.) ICALP 2002. LNCS, vol. 2380, pp. 318–329. Springer, Heidelberg (2002)
Patil, S.S.: Coordination of asynchronous events. Ph.D. thesis, MIT (1970)
Patitz, M.J., Summers, S.M.: Self-assembly of decidable sets. In: Calude, C.S., Costa, J.F., Freund, R., Oswald, M., Rozenberg, G. (eds.) UC 2008. LNCS, vol. 5204, pp. 206–219. Springer, Heidelberg (2008)
Păun, G.: Computing with membranes. J. Comput. Syst. Sci. 1(61), 108–143 (2000). Also TUCS Report No. 208, 1998
Păun, G.: Membrane Computing: An Introduction. Springer, Heidelberg (2002)
Păun, G., Rozenberg, G., Salomaa, A.: DNA Computing: New Computing Paradigms. Springer, Heidelberg (1998)
Păun, G., Rozenberg, G., Salomaa, A.: The Oxford Handbook Of Membrane Computing. Oxford University Press, New York (2009)
Qian, L., Soloveichik, D., Winfree, E.: Efficient turing-universal computation with DNA polymers. In: Sakakibara, Y., Mi, Y. (eds.) DNA 16 2010. LNCS, vol. 6518, pp. 123–140. Springer, Heidelberg (2011)
Rogozhin, Y.: Small universal turing machines. Theor. Comput. Sci. 168(2), 215–240 (1996)
Rozenberg, G., Bäck, T., Kok, J.N. (eds.): Handbook of Natural Computing. Springer, Heidelberg (2012)
Rozenberg, G., Salomaa, A.: Handbook of Formal Languages. Springer, Heidelberg (1997)
Schroeppel, R.: A two counter machine cannot calculate 2N. AI Memos, Cambridge (1972)
Seelig, G., Soloveichik, D., Zhang, D.Y., Winfree, E.: Enzyme-free nucleic acid logic circuits. Science 314(5805), 1585–1588 (2006)
Shannon, C.E.: A universal Turing machine with two internal states. Autom. Stud. Ann. Math. Stud. 34, 157–165 (1956)
Soloveichik, D., Winfree, E.: Complexity of self-assembled shapes. SIAM J. Comput. 36(6), 1544–1569 (2007)
Turing, A.M.: On computable numbers, with an application to the Entscheidungsproblem. Proc. Lond. Math. Soc. 42(2), 230–265 (1936)
Verlan, S.: Study of language-theoretic computational paradigms inspired by biology. Habilitation thesis, Université Paris Est (2010)
von Neumann, J.: Theory of self-reproducing automata. University of Illinois (1966)
Watanabe, S.: 5-symbol 8-state and 5-symbol 6-state universal turing machines. J. ACM 8(4), 476–483 (1961)
Winfree, E.: Algorithmic self-assembly of DNA. Ph.D. thesis, Caltech (1998)
Wolfram, S.: A New Kind of Science. Wolfram Media Inc., UK (2002)
Zizza, R.: Splicing systems. Scholarpedia 5(7), 9397 (2010)
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Verlan, S. (2015). Universality in Molecular and Cellular Computing. In: Beckmann, A., Mitrana, V., Soskova, M. (eds) Evolving Computability. CiE 2015. Lecture Notes in Computer Science(), vol 9136. Springer, Cham. https://doi.org/10.1007/978-3-319-20028-6_10
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