Abstract
The transitions of a stateless automaton do not depend on internal states but solely on the symbols currently scanned by its head accessing the input and memory. We investigate stateless deterministic restarting automata that, after executing a rewrite step, continue to read their tape before performing a restart. Even the weakest class thus obtained contains the regular languages properly. The relations between different classes of stateless automata as well as between stateless automata and the corresponding types of automata with states are investigated, and it is shown that the language classes defined by the various types of deterministic stateless restarting automata without auxiliary symbols are anti-AFLs that are not even closed under reversal.
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References
Buntrock G., Otto F.: Growing context-sensitive languages and Church-Rosser languages. Inform. Comput. 141, 1–36 (1998)
Culy C.: Formal properties of natural language and linguistic theories. Linguist. Philos. 19, 599–617 (1996)
Frisco, P., Ibarra, O.H.: On stateless multihead finite automata and multihead pushdown automata. In: Diekert, V., Nowotka, D. (eds.) DLT 2009, Proceedings, Lecture Notes in Computer Science, vol. 5583, pp. 240–251. Springer, Berlin (2009)
Holzer M., Kutrib M., Reimann J.: Non-recursive trade-offs for deterministic restarting automata. J. Autom. Lang. Comb. 12, 195–213 (2007)
Harrison M.: Introduction to Formal Language Theory. Addison-Wesley, Reading, MA (1978)
Ibarra O.H., Dang Z., Egecioglu Ö.: Catalytic P systems, semilinear sets, and vector addition systems. Theor. Comput. Sci. 312, 379–399 (2004)
Ibarra O.H., Karhumäki J., Okhotin A.: On stateless multihead automata: Hierarchies and the emptiness problem. In: Laber, E.S., Bornstein, C., Nogueira, L.T., Faria, L. (eds) LATIN 2008, Proceedings, Lecture Notes in Computer Science, vol. 4957, pp. 94–105. Springer, Berlin (2008)
Jančar P., Mráz F., Plátek M., Vogel J.: Restarting automata. In: Reichel, H. (eds) FCT 1995, Proceedings, Lecture Notes in Computer Science, vol. 965, pp. 283–292. Springer, Berlin (1995)
Kutrib M., Messerschmidt H., Otto F.: On stateless two-pushdown automata and restarting automata. In: Csuhaj-Varjú, E., Ésik, Z. (eds) Automata and Formal Languages, AFL 2008, Proceedings, pp. 257–268. Computer and Automation Research Institute, Hungarian Academy of Sciences, Budapest (2008)
Kutrib M., Messerschmidt H., Otto F.: On stateless deterministic restarting automata. In: Nielsen, M., Kučera, A., Miltersen, P.B., Palamidessi, C., Tuma, P., Valencia, F. (eds) SOFSEM 2009: Theory and Practice of Computer Science, Proceedings, Lecture Notes in Computer Science, vol. 5404, pp. 353–364. Springer, Berlin (2009)
Kutrib, M., Messerschmidt, H. Otto, F.: On stateless two-pushdown automata and restarting automata. Extended version of Kutrib et al. (2008). (Submitted for publication)
Kutrib M., Reimann J.: Succinct description of regular languages by weak restarting automata. Inform. Comput. 206, 1152–1160 (2008)
Niemann G., Otto F.: The Church-Rosser languages are the deterministic variants of the growing context-sensitive languages. Inform. Comput. 197, 1–21 (2005)
Otto F.: Restarting automata. In: Ésik, Z., Martin-Vide, C., Mitrana, V. (eds) Recent Advances in Formal Languages and Applications, Studies in Computational Intelligence, vol. 25, pp. 269–303. Springer, Berlin (2006)
Rabin M.O., Scott D.: Finite automata and their decision problems. IBM J. Res. Dev. 3, 114–125 (1959)
Yang, L., Dang, Z., Ibarra, O.H.: On stateless automata and P systems. In: Workshop on Automata for Cellular and Molecular Computing, MTA SZTAKI, pp. 144–157 (2007)
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The results of this paper have been announced at SOFSEM 2009 in Špindler\({\stackrel{\circ}{\rm u}}\)v Mlýn, January 2009. An extended abstract appeared in the proceedings of that conference [10].
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Kutrib, M., Messerschmidt, H. & Otto, F. On stateless deterministic restarting automata. Acta Informatica 47, 391–412 (2010). https://doi.org/10.1007/s00236-010-0125-4
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DOI: https://doi.org/10.1007/s00236-010-0125-4