Abstract
Recently, new types of non-sequential machine models have been introduced and studied, such as jumping automata and one-way jumping automata. We study the abilities and limitations of (finite, pushdown and linear bounded) automata with these 2 jumping modes of tape heads with respect to how they affect the class of accepted languages. We provide adapted versions of pumping lemmas and other methods to determine whether a language is accepted by a machine with jumping mode. Using these methods we establish the inclusion or incomparability relationships among the classes of languages defined by the new machines and their classical counterparts. We also study the closure properties of the resulting language classes and show that under most fundamental language operations, these classes are not closed.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Beier S, Holzer M (2018) Decidability of right one-way jumping finite automata. In: Hoshi M, Seki S (eds.) Developments in Language Theory - 22nd International Conference, DLT 2018, Tokyo, Japan, September 10-14, 2018, Proceedings, Lecture Notes in Computer Science 11088: 109–120. Springer. https://doi.org/10.1007/978-3-319-98654-8_9
Beier S, Holzer M (2019) Nondeterministic right one-way jumping finite automata (extended abstract). In: Hospodár M, Jirásková G, Konstantinidis S (eds) Descriptional complexity of formal systems. Springer, Cham, pp 74–85
Beier S, Holzer M (2019) Properties of right one-way jumping finite automata. Theor Comput Sci 798:78–94
Beier S, Holzer M, Kutrib M (2017) Operational state complexity and decidability of jumping finite automata. In: É. Charlier, J. Leroy, M. Rigo (eds.) Developments in Language Theory - 21st International Conference, DLT 2017, Liège, Belgium, August 7-11, 2017, Proceedings, Lecture Notes in Computer Science, vol. 10396, pp. 96–108. Springer. https://doi.org/10.1007/978-3-319-62809-7_6
Chigahara H, Fazekas SZ, Yamamura A (2016) One-way jumping finite automata. Int J Found Comput Sci 27(3):391–405. https://doi.org/10.1142/S0129054116400165
Fazekas SZ, Hoshi K, Yamamura A (2019) Enhancement of automata with jumping modes. In: Castillo-Ramirez A, de Oliveira PPB (eds) Cellular automata and discrete complex systems. Springer, Cham, pp 62–76
Fazekas SZ, Hoshi K, Yamamura A (2020) Two-way jumping automata. In: M. Li (ed.) Frontiers in Algorithmics - 14th International Workshop, FAW 2020, Haikou, China, October 19-21, 2020, Proceedings, Lecture Notes in Computer Science, vol. 12340, pp. 108–120. Springer. https://doi.org/10.1007/978-3-030-59901-0_10
Fazekas SZ, Yamamura A (2016) On regular languages accepted by one-way jumping finite automata. In: 8th NCMA, Debrecen, Hungary, Short Papers, pp. 7–14. sterreichische Computer Gesellschaft
Fernau H, Paramasivan M, Schmid ML (2015) Jumping finite automata: Characterizations and complexity. In: Drewes F (ed.) Implementation and Application of Automata - 20th International Conference, CIAA 2015, Umeå, Sweden, August 18-21, 2015, Proceedings, Lecture Notes in Computer Science, vol. 9223, pp. 89–101. Springer (2015). https://doi.org/10.1007/978-3-319-22360-5_8
Fernau H, Paramasivan M, Schmid ML, Vorel V (2017) Characterization and complexity results on jumping finite automata. Theor Comput Sci 679:31–52. https://doi.org/10.1016/j.tcs.2016.07.006
Hopcroft JE, Ullman JD (1979) Introduction to Automata Theory. Addison-Wesley, Languages and Computation
Kocman R, Meduna A (2016) On parallel versions of jumping finite automata. In: Janech J, Kostolny J, Gratkowski T (eds) Advances in Intelligent Systems and Computing, Springer, Berlin, pp. 142–149. https://doi.org/10.1007/978-3-319-46535-7_12
Krivka Z, Meduna A (2015) Jumping grammars. Int J Found Comput Sci 26(6):709–732. https://doi.org/10.1142/S0129054115500409
Latteux M (1979) Cônes rationnels commutatifs. J Comput Syst Sci 18(3):307–333. https://doi.org/10.1016/0022-0000(79)90039-4
Madejski G (2016) Jumping and pumping lemmas and their applications. In: Eighth Workshop on Non-Classical Models of Automata and Applications (NCMA 2016) Short papers, pp. 25–33
Meduna A, Zemek P (2012) Jumping finite automata. Int J Found Comput Sci 23(7):1555–1578. https://doi.org/10.1142/S0129054112500244
Meduna A, Zemek P (2014) Regulated grammars and automata. Springer. https://doi.org/10.1007/978-1-4939-0369-6
Parikh R (1966) On context-free languages. J. ACM 13(4):570–581. https://doi.org/10.1145/321356.321364
Sipser M (2006) Introduction to the Theory of Computation, second edn. Course Technology
Yu S (1989) A pumping lemma for deterministic context-free languages. Inf Process Lett 31(1):47–51. https://doi.org/10.1016/0020-0190(89)90108-7
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Fazekas, S.Z., Hoshi, K. & Yamamura, A. The effect of jumping modes on various automata models. Nat Comput 21, 17–30 (2022). https://doi.org/10.1007/s11047-021-09844-4
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11047-021-09844-4