Reaction automata working in sequential manner
Okubo, Fumiya
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 48 (2014), p. 23-38 / Harvested from Numdam
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Based on the formal framework of reaction systems by Ehrenfeucht and Rozenberg [Fund. Inform. 75 (2007) 263-280], reaction automata (RAs) have been introduced by Okubo et al. [Theoret. Comput. Sci. 429 (2012) 247-257], as language acceptors with multiset rewriting mechanism. In this paper, we continue the investigation of RAs with a focus on the two manners of rule application: maximally parallel and sequential. Considering restrictions on the workspace and the λ-input mode, we introduce the corresponding variants of RAs and investigate their computation powers. In order to explore Turing machines (TMs) that correspond to RAs, we also introduce a new variant of TMs with restricted workspace, called s(n)-restricted TMs. The main results include the following: (i) for a language L and a function s(n), L is accepted by an s(n)-bounded RA with λ-input mode in sequential manner if and only if L is accepted by a log s(n)-bounded one-way TM; (ii) if a language L is accepted by a linear-bounded RA in sequential manner, then L is also accepted by a P automaton [Csuhaj-Varju and Vaszil, vol. 2597 of Lect. Notes Comput. Sci. Springer (2003) 219-233.] in sequential manner; (iii) the class of languages accepted by linear-bounded RAs in maximally parallel manner is incomparable to the class of languages accepted by RAs in sequential manner.

Publié le : 2014-01-01
DOI : https://doi.org/10.1051/ita/2013047
Classification:  68Q05,  68Q45 
@article{ITA_2014__48_1_23_0,
     author = {Okubo, Fumiya},
     title = {Reaction automata working in sequential manner},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     volume = {48},
     year = {2014},
     pages = {23-38},
     doi = {10.1051/ita/2013047},
     mrnumber = {3195787},
     language = {en},
     url = {http://dml.mathdoc.fr/item/ITA_2014__48_1_23_0}
}

Okubo, Fumiya. Reaction automata working in sequential manner. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 48 (2014) pp. 23-38. doi : 10.1051/ita/2013047. http://gdmltest.u-ga.fr/item/ITA_2014__48_1_23_0/

[1] C. Calude, Gh. Păun, G. Rozenberg and A. Salomaa, Multiset Processing. In vol. 2235 of Lect. Notes Comput. Sci. Springer (2001). | MR 2054251 | Zbl 0983.00053

[2] E. Csuhaj-Varjú, O.H. Ibarra and Gy. Vaszil, On the computational complexity of P automata. Nat. Comput. 5 (2006) 109-126. | MR 2259031 | Zbl 1112.68057

[3] E. Csuhaj-Varjú, M. Oswald and Gy. Vaszil, P automata, in The Oxford Handbook of Membrane Computing (2010) 145-167.

[4] E. Csuhaj-Varjú and Gy. Vaszil, P automata or purely communicating accepting P systems. In vol. 2597 of Lect. Notes Comput. Sci. Springer (2003) 219-233. | MR 2048885 | Zbl 1023.68039

[5] A. Ehrenfeucht and G. Rozenberg, Reaction systems. Fund. Inform. 75 (2007) 263-280. | MR 2293699 | Zbl 1108.68056

[6] A. Ehrenfeucht and G. Rozenberg, Events and modules in reaction systems. Theoret. Comput. Sci. 376 (2007) 3-16. | MR 2316386 | Zbl 1119.93011

[7] A. Ehrenfeucht and G. Rozenberg, Introducing time in reaction systems. Theoret. Comput. Sci. 410 (2009) 310-322. | MR 2493981 | Zbl 1156.93306

[8] A. Ehrenfeucht, M. Main and G. Rozenberg, Combinatorics of life and death in reaction systems. Int. J. Found. Comput. Sci. 21 (2010) 345-356. | MR 2653855 | Zbl 1192.68458

[9] A. Ehrenfeucht, M. Main and G. Rozenberg, Functions defined by reaction systems. Int. J. Found. Comput. Sci. 22 (2011) 167-178. | MR 2764626 | Zbl 1213.68259

[10] P.C. Fischer, Turing Machines with Restricted Memory Access. Inform. Control 9 (1966) 364-379. | MR 199061 | Zbl 0145.24205

[11] M. Hirvensalo, On probabilistic and quantum reaction systems. Theoret. Comput. Sci. 429 (2012) 134-143. | MR 2901403 | Zbl 1248.68197

[12] J.E. Hopcroft, T. Motwani and J.D. Ullman, Introduction to automata theory, language and computation, 2nd edition. Addison-Wesley (2003). | MR 645539 | Zbl 0980.68066

[13] M. Kudlek, C. Martin-Vide and Gh. Păun, Toward a formal macroset theory, in Multiset Processing, vol. 2235 of Lect. Notes Comput. Sci., edited by C. Calude, Gh. Păun, G. Rozenberg and A. Salomaa. Springer (2001) 123-134. | MR 2054257 | Zbl 1052.68063

[14] F. Okubo, On the Computational Power of Reaction Automata Working in Sequential Manner, in Proc. of 4th Workshop on Non-Classical Models for Automata and Applications, vol. 290 of book@ocg.at series. Öesterreichische Comput. Gesellschaft (2012) 149-164.

[15] F. Okubo, S. Kobayashi and T. Yokomori, Reaction Automata. Theoret. Comput. Sci. 429 (2012) 247-257. | MR 2901416 | Zbl 1276.68074

[16] F. Okubo, S. Kobayashi and T. Yokomori, On the Properties of Language Classes Defined by Bounded Reaction Automata. Theoret. Comput. Sci. 454 (2012) 206-221. | MR 2966636 | Zbl 1252.68180

[17] A. Salomaa, Formal Languages. Academic Press, New York (1973). | MR 438755 | Zbl 0686.68003

[18] A. Salomaa, Functions and sequences generated by reaction systems. Theoret. Comput. Sci. 466 (2012) 87-96. | MR 2997425 | Zbl pre06137324