Abstract
We use weighted restarting automata to define classes of formal languages by combining the acceptance condition of a restarting automaton with a condition on the weight of its accepting computations. Specifically, we consider the tropical semiring \(\mathbb {Z}_\infty \) and the semiring \(\mathsf{REG}({\varDelta })\) of regular languages over a finite alphabet \({\varDelta }\). We show that by using the tropical semiring, we can avoid the use of auxiliary symbols. Further, a certain type of (word-) weighted restarting automata turns out to be equivalent to non-forgetting restarting automata, and another class of languages accepted by (word-) weighted restarting automata is shown to be closed under intersection.
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Jancar, P., Mráz, F., Plátek, M., Vogel, J.: Restarting automata. In: Reichel, H. (ed.) FCT 1995. LNCS, vol. 965, pp. 283–292. Springer, Heidelberg (1995)
Jancar, P., Mráz, F., Plátek, M., Vogel, J.: On monotonic automata with a restart operation. J. Auto. Lang. Comb. 4(4), 287–312 (1999)
Jurdziński, T., Lorys, K., Niemann, G., Otto, F.: Some results on RWW- and RRWW-automata and their relation to the class of growing context-sensitive languages. J. Autom. Lang. Comb. 9(4), 407–437 (2004)
Messerschmidt, H., Otto, F.: Cooperating distributed systems of restarting automata. Int. J. Found. Comput. Sci. 18, 1333–1342 (2007)
Messerschmidt, H., Stamer, H.: Restart-Automaten mit mehreren Restart-Zuständen. In: Bordihn, H. (ed.) Workshop “Formale Methoden in der Linguistik” und 14. Theorietag “Automaten und Formale Sprachen”. pp. 111–116. Institut für Informatik, Universität Potsdam, Potsdam (2004)
Messerschmidt, H.: CD-Systems of restarting automata. Ph.D. thesis, Fachbereich Elektrotechnik/Informatik, Universität Kassel (2008)
Messerschmidt, H., Otto, F.: On nonforgetting restarting automata that are deterministic and/or monotone. In: Grigoriev, D., Harrison, J., Hirsch, E.A. (eds.) CSR 2006. LNCS, vol. 3967, pp. 247–258. Springer, Heidelberg (2006)
Otto, F.: Restarting automata. In: Ésik, Z., Martín-Vide, C., Mitrana, V. (eds.) Recent Advances in Formal Languages and Applications, vol. 25, pp. 269–303. Springer, Heidelberg (2006)
Otto, F., Wang, Q.: Weighted restarting automata. Soft Computing (2016). Accepted. The results of this paper have been announced at WATA 2014 in Leipzig. doi:10.1007/s00500-016-2164-4
Wang, Q., Hundeshagen, N., Otto, F.: Weighted restarting automata and pushdown relations. In: Maletti, A. (ed.) Algebraic Informatics. LNCS, vol. 9270, pp. 196–207. Springer, Switzerland (2015)
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Wang, Q., Otto, F. (2016). Weighted Restarting Automata as Language Acceptors. In: Han, YS., Salomaa, K. (eds) Implementation and Application of Automata. CIAA 2016. Lecture Notes in Computer Science(), vol 9705. Springer, Cham. https://doi.org/10.1007/978-3-319-40946-7_25
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DOI: https://doi.org/10.1007/978-3-319-40946-7_25
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