Abstract
We propose a new computing model called chemical reaction automata (CRAs) as a simplified variant of reaction automata (RAs) studied in recent literature (Okubo in RAIRO Theor Inform Appl 48:23–38 2014; Okubo et al. in Theor Comput Sci 429:247–257 2012a, Theor Comput Sci 454:206–221 2012b). We show that CRAs in maximally parallel manner are computationally equivalent to Turing machines, while the computational power of CRAs in sequential manner coincides with that of the class of Petri nets, which is in marked contrast to the result that RAs (in both maximally parallel and sequential manners) have the computing power of Turing universality (Okubo 2014; Okubo et al. 2012a). Intuitively, CRAs are defined as RAs without inhibitor functioning in each reaction, providing an offline model of computing by chemical reaction networks (CRNs). Thus, the main results in this paper not only strengthen the previous result on Turing computability of RAs but also clarify the computing powers of inhibitors in RA computation.
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Notes
This trick has been used for simulating M by an RA (with inhibitor) in sequential manner in Okubo (2014).
References
Angluin D, Aspnes J, Eisenstat D (2006) Stably computable predicates are semilinear. In: Proceedings of the 25th annual ACM symposium on principles of distributed computing. ACM Press, New York, pp 292–299
Calude C, Păun G, Rozenberg G, Salomaa A (eds.) (2001) Multiset processing. LNCS, vol 2235. Springer, Heidelberg
Chen H-L, Doty D, Soloveichik D (2012) Deterministic function computation with chemical reaction networks. In: Stefanovic D, Turberfield A (eds) DNA 18, LNCS. Springer, Heidelberg, pp 25–42
Csuhaj-Varju E, Ibarra OH, Vaszil G (2006) On the computational complexity of P automata. Nat Comput 5:109–126
Csuhaj-Varju E, Vaszil G (2010) P automata. In: Păun G, Rozenberg G, Salomaa A (eds) The oxford handbook of membrane computing. Oxford University Press, New York, pp 145–167
Csuhaj-Varju E, Vaszil G (2003) P automata or purely communicating accepting P systems. In: Păun G, Rozenberg G, Salomaa A, Zandron C (eds) LNCS, vol 2597. Springer, Berlin, pp 219–233
Ehrenfeucht A, Rozenberg G (2007) Reaction systems. Fundam Inform 75:263–280
Fischer PC (1966) Turing machines with restricted memory access. Inform Control 9(4):364–379
Hopcroft JE, Motwani T, Ullman JD (2003) Introduction to automata theory, language and computation, 2nd edn. Addison-Wesley, Boston
Kudlek M, Martin-Vide C, Păun G (2001) Toward a formal macroset theory. In: Calude C, Păun G, Rozenberg G, Salomaa A (eds) Multiset processing, LNCS. Springer, New York, pp 123–134
Okubo F (2014) Reaction automata working in sequential manner. RAIRO Theor Inform Appl 48:23–38
Okubo F, Kobayashi S, Yokomori T (2012a) Reaction automata. Theor Comput Sci 429:247–257
Okubo F, Kobayashi S, Yokomori T (2012b) On the properties of language classes defined by bounded reaction automata. Theor Comput Sci 454:206–221
Okubo F, Yokomori T (2014) The computational capability of chemical reaction automata. In: Murata S, Kobayashi S (eds) DNA20, LNCS. Springer, Switzerland, pp 53–66
Peterson JL (1981) Petri net theory and the modelling of systems. Prentice-Hall, Englewood Cliffs
Qian L, Soloveichik D, Winfree E (2011) Efficient turing-universal computation with DNA polymers. In: Sakakibara Y, Mi Y (eds) DNA16, LNCS. Springer, Heidelberg, pp 123–140
Soloveichik D, Cook M, Winfree E, Bruck J (2008) Computation with finite stochastic chemical reaction networks. Nat Comput 7(4):615–633
Suzuki Y, Fujiwara Y, Takabayashi J, Tanaka H (2001) Artificial life applications of a class of P systems: abstract rewriting systems on multisets. In: Calude C, Păun G, Rozenberg G, Salomaa A (eds) Multiset processing, LNCS. Springer, Heidelberg, pp 299–346
Thachuk C, Condon A (2012) Space and energy efficient computation with DNA strand displacement systems. In: Stefanovic D, Turberfield A (eds) DNA 18, LNCS, vol 7433. Springer, Heidelberg, pp 135–149
Acknowledgments
The work of F. Okubo was in part supported by Grants-in-Aid for JSPS Fellows No. 25.3528, Japan Society for the Promotion of Science. The work of T. Yokomori was in part supported by a Grant-in-Aid for Scientific Research on Innovative Areas “Molecular Robotics” (No. 24104003) of The Ministry of Education, Culture, Sports, Science, and Technology, Japan, and by Waseda University grant for Special Research Projects: 2013B-063 and 2013C-159.
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This paper is an extension of the conference paper titled “The computational Capability of Chemical Reaction Automata” (Okubo and Yokomori 2014).
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Okubo, F., Yokomori, T. The computational capability of chemical reaction automata. Nat Comput 15, 215–224 (2016). https://doi.org/10.1007/s11047-015-9504-7
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DOI: https://doi.org/10.1007/s11047-015-9504-7