Abstract
We characterize the class of languages described by jumping finite automata (i. e., finite automata, for which the input head after reading (and consuming) a symbol, can jump to an arbitrary position of the remaining input) in terms of special shuffle expressions. We can characterize some interesting subclasses of this language class. The complexity of parsing these languages is also investigated.
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Notes
- 1.
We wish to point out that this also follows from results in [1], where containment in NP is shown for a superclass of \(\mathscr {JFA}\).
References
Crespi-Reghizzi, S., San Pietro, P.: Commutative languages and their composition by consensual methods. In: Ésik, V., Fülöp, Z. (eds.) Proceedings 14th International Conference on Automata and Formal Languages (AFL), vol. 151 of EPTCS, pp. 216–230 (2014)
Downey, R.G., Fellows, M.R.: Fundamentals of Parameterized Complexity. Texts in Computer Science. Springer, Heidelberg (2013)
Eggan, L.C.: Transition graphs and the star-height of regular events. Mich. Math. J. 10(4), 385–397 (1963)
Ehrenfeucht, A., Haussler, D., Rozenberg, G.: On regularity of context-free languages. Theor. Comput. Sci. 27, 311–332 (1983)
Esparza, J., Ganty, P., Kiefer, S., Luttenberger, M.: Parikh’s theorem: A simple and direct automaton construction. Inf. Process. Lett. 111(12), 614–619 (2011)
Hashiguchi, K.: Algorithms for determining relative star height and star height. Inf. Comput. 78(2), 124–169 (1988)
Höpner, M., Opp, M.: About three equations classes of languages built up by shuffle operations. In: Mazurkiewicz, A.W. (ed.) MFCS 1976. LNCS, vol. 45, pp. 337–344. Springer, Heidelberg (1976)
Jantzen, M.: Eigenschaften von Petrinetzsprachen. Technical report IFI-HH-B-64, Fachbereich Informatik, Universität Hamburg, Germany (1979)
Jantzen, M.: The power of synchronizing operations on strings. Theor. Comput. Sci. 14, 127–154 (1981)
Jantzen, M.: Extending regular expressions with iterated shuffle. Theor. Comput. Sci. 38, 223–247 (1985)
Jedrzejowicz, J., Szepietowski, A.: Shuffle languages are in P. Theor. Comput. Sci. 250(1–2), 31–53 (2001)
Jiang, H., Su, B., Xiao, M., Xu, Y., Zhong, F., Zhu, B.: On the exact block cover problem. In: Gu, Q., Hell, P., Yang, B. (eds.) AAIM 2014. LNCS, vol. 8546, pp. 13–22. Springer, Heidelberg (2014)
Klíma, O., Polák, L.: On biautomata. RAIRO Informatique théorique et Appl. Theor. Inf. Appl. 46, 573–592 (2012)
Latteux, M., Rozenberg, G.: Commutative one-counter languages are regular. J. Comput. Sys. Sci. 1, 54–57 (1984)
Meduna, A., Zemek, P.: Jumping finite automata. Int. J. Found. Comput. Sci. 23(7), 1555–1578 (2012)
Meduna, A., Zemek, P.: Chapter 17: Jumping finite automata. In: Meduna, A., Zemek, P. (eds.) Regulated Grammars and Automata, pp. 567–585. Springer, New York (2014)
Otto, F.: Restarting automata. In: Ésik, Z., Martín-Vide, C., Mitrana, V. (eds.) FCT 1995, vol. 965, pp. 269–303. Springer, Heidelberg (2006)
Parikh, R.J.: On context-free languages. J. ACM 13(4), 570–581 (1966)
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Fernau, H., Paramasivan, M., Schmid, M.L. (2015). Jumping Finite Automata: Characterizations and Complexity. In: Drewes, F. (eds) Implementation and Application of Automata. CIAA 2015. Lecture Notes in Computer Science(), vol 9223. Springer, Cham. https://doi.org/10.1007/978-3-319-22360-5_8
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DOI: https://doi.org/10.1007/978-3-319-22360-5_8
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