Abstract
We propose a new variant of Accepting Networks of Evolutionary Processors, in which the operations are applied at arbitrary positions to the processed words (rather than at the ends of words only) and where the filters are languages from several special classes of regular sets. More precisely, we show that the use of filters from the class of non-counting, ordered, power-separating, suffix-closed regular, union-free, definite and combinational languages is as powerful as the use of arbitrary regular languages and yields networks that can accept all the recursively enumerable languages. On the other hand, by using filters that are only finite languages, monoids, nilpotent languages, commutative regular languages, or circular regular languages, one cannot generate all recursively enumerable languages. These results seem interesting as they provide both upper and lower bounds on the classes of languages that one can use as filters in an accepting network of evolutionary processors in order to obtain a complete computational model.
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References
Csuhaj-Varjú, E., Mitrana, V.: Evolutionary systems: a language generating device inspired by evolving communities of cells. Acta Inform. 36(11), 913–926 (2000)
Csuhaj-Varjú, E., Salomaa, A.: Networks of parallel language processors. In: New Trends in Formal Languages—Control, Cooperation, and Combinatorics. LNCS, vol. 1218, pp. 299–318. Springer, Berlin (1997)
Dassow, J., Truthe, B.: On networks of evolutionary processors with state limited filters. In: Bordihn, H., Freund, R., Hinze, T., Holzer, M., Kutrib, M., Otto, F. (eds.) Second Workshop on Non-Classical Models of Automata and Applications (NCMA), Proceedings, Jena, Germany, August 23–24, 2010. books@ocg.at, vol. 263, pp. 57–70. Österreichische Computer Gesellschaft, Vienna (2010)
Dassow, J., Truthe, B.: On networks of evolutionary processors with filters accepted by two-state-automata. Fundam. Inform. 112(2–3), 157–170 (2011)
Dassow, J., Manea, F., Truthe, B.: Networks of evolutionary processors with subregular filters. In: Dediu, A.H., Inenaga, S., Martín-Vide, C. (eds.) 5th International Conference on Language and Automata Theory and Applications (LATA), Proceedings, Tarragona, Spain, May 26–31, 2011. LNCS, vol. 6638, pp. 262–273. Springer, Berlin (2011)
Dassow, J., Manea, F., Truthe, B.: Networks of evolutionary processors: the power of subregular filters. Acta Inform. 50(1), 41–75 (2013)
Errico, L.D., Jesshope, C.: Towards a new architecture for symbolic processing. In: Proc. of AIICSR’94, pp. 31–40. World Scientific Publishing Co., Inc., River Edge (1994)
Fahlman, S.E., Hinton, G.E., Sejnowski, T.J.: Massively parallel architectures for AI: NETL, thistle, and Boltzmann machines. In: Proc. AAAI, vol. 1983, pp. 109–113 (1983)
Havel, I.M.: The theory of regular events II. Kybernetika 5(6), 520–544 (1969)
Hillis, W.D.: The Connection Machine. MIT Press, Cambridge (1986)
Kuroda, S.Y.: Classes of languages and linear-bounded automata. Inf. Control 7(2), 207–223 (1964)
Manea, F., Martín-Vide, C., Mitrana, V.: On the size complexity of universal accepting hybrid networks of evolutionary processors. Math. Struct. Comput. Sci. 17(4), 753–771 (2007)
Manea, F., Martín-Vide, C., Mitrana, V.: Accepting networks of evolutionary word and picture processors: a survey. In: Martín-Vide, C. (ed.) Scientific Applications of Language Methods, Mathematics, Computing, Language, and Life: Frontiers in Mathematical Linguistics and Language Theory, vol. 2, pp. 525–560. World Scientific, Singapore (2010)
Manea, F., Margenstern, M., Mitrana, V., Pérez-Jiménez, M.J.: A new characterization of NP, P and PSPACE with accepting hybrid networks of evolutionary processors. Theory Comput. Syst. 46(2), 174–192 (2010)
Margenstern, M., Mitrana, V., Pérez-Jiménez, M.J.: Accepting hybrid networks of evolutionary processors. In: DNA Computing, 10th International Workshop on DNA Computing. LNCS, vol. 3384, pp. 235–246. Springer, Berlin (2004)
Păun, G.: Computing with membranes. J. Comput. Syst. Sci. 61(1), 108–143 (2000)
Păun, G., Sântean, L.: Parallel communicating grammar systems: the regular case. Ann. Univ. Buchar., Ser. Mat. Inform. 38, 55–63 (1989)
Rozenberg, G., Salomaa, A.: Handbook of Formal Languages. Springer, Berlin (1997)
Sankoff, D., Leduc, G., Antoine, N., Paquin, B., Lang, F., Cedergren, R.: Gene order comparisons for phylogenetic inference: evolution of the mitochondrial genome. Proc. Natl. Acad. Sci. USA 89(14), 6575–6579 (1992)
Wiedemann, B.: Vergleich der Leistungsfähigkeit endlicher determinierter Automaten. Diplomarbeit, Universität Rostock (1978)
Acknowledgements
We thank Jürgen Dassow for discussions and ideas on this topic as well as the anonymous referees for their suggestions.
The paper was partly written when Florin Manea was a Research Fellow of the Alexander von Humboldt Foundation at the Otto-von-Guericke-Universität Magdeburg, whose support is acknowledged. Florin Manea’s work is currently supported by the DFG grant 582014.
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This paper is an extended version of the paper presented at the international conference Automata and Formal Languages (AFL) in Debrecen, Hungary, 2011.
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Manea, F., Truthe, B. Accepting Networks of Evolutionary Processors with Subregular Filters. Theory Comput Syst 55, 84–109 (2014). https://doi.org/10.1007/s00224-013-9502-z
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DOI: https://doi.org/10.1007/s00224-013-9502-z