Abstract
We examine the succinctness of one-way, rotating, sweeping, and two-way deterministic finite automata (1dfas, rdfas, sdfas, 2dfas). Here, a sdfa is a 2dfa whose head can change direction only on the endmarkers and a rdfa is a sdfa whose head is reset on the left end of the input every time the right endmarker is read. We introduce a list of language operators and study the corresponding closure properties of the size complexity classes defined by these automata. Our conclusions reveal the logical structure of certain proofs of known separations in the hierarchy of these classes and allow us to systematically construct alternative problems to witness these separations.
Work supported by the Swiss National Science Foundation grant 200021-107327/1.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Berman, P.: A note on sweeping automata. In: de Bakker, J.W., van Leeuwen, J. (eds.) ICALP 1980. LNCS, vol. 85, pp. 91–97. Springer, Heidelberg (1980)
Geffert, V., Mereghetti, C., Pighizzini, G.: Complementing two-way finite automata. Information and Computation 205(8), 1173–1187 (2007)
Kapoutsis, C., Královič, R., Mömke, T.: An exponential gap between LasVegas and deterministic sweeping finite automata. In: Hromkovič, J., Královič, R., Nunkesser, M., Widmayer, P. (eds.) SAGA 2007. LNCS, vol. 4665, pp. 130–141. Springer, Heidelberg (2007)
Micali, S.: Two-way deterministic finite automata are exponentially more succinct than sweeping automata. Information Processing Letters 12(2), 103–105 (1981)
Sakoda, W.J., Sipser, M.: Nondeterminism and the size of two way finite automata. In: Proceedings of the 10th Annual ACM Symposium on Theory of Computing, San Diego, California, USA, May 1-3, 1978. ACM, New York (1978)
Seiferas, J.I.: Untitled manuscript. Communicated to Michael Sipser (October 1973)
Sipser, M.: Lower bounds on the size of sweeping automata. Journal of Computer and System Sciences 21(2), 195–202 (1980)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kapoutsis, C., Královič, R., Mömke, T. (2008). On the Size Complexity of Rotating and Sweeping Automata. In: Ito, M., Toyama, M. (eds) Developments in Language Theory. DLT 2008. Lecture Notes in Computer Science, vol 5257. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85780-8_36
Download citation
DOI: https://doi.org/10.1007/978-3-540-85780-8_36
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-85779-2
Online ISBN: 978-3-540-85780-8
eBook Packages: Computer ScienceComputer Science (R0)