Abstract
On every n-long input, every two-way finite automaton (2fa) can reverse its head O(n) times before halting. A 2FA with few reversals is an automaton where this number is only o(n). For every h, we exhibit a language that requires Ω(2h) states on every deterministic 2FA with few reversals, but only h states on a nondeterministic 2FA with few reversals.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Berman, P., Lingas, A.: On complexity of regular languages in terms of finite automata. Report 304, Institute of Computer Science, Polish Academy of Sciences, Warsaw (1977)
Geffert, V., Mereghetti, C., Pighizzini, G.: Converting two-way nondeterministic unary automata into simpler automata. Theoretical Computer Science 295, 189–203 (2003)
Geffert, V., Pighizzini, G.: Two-way unary automata versus logarithmic space. In: Gao, Y., Lu, H., Seki, S., Yu, S. (eds.) DLT 2010. LNCS, vol. 6224, pp. 197–208. Springer, Heidelberg (2010)
Hromkovič, J.: Descriptional complexity of finite automata: concepts and open problems. Journal of Automata, Languages and Combinatorics 7(4), 519–531 (2002)
Hromkovič, J., Schnitger, G.: Nondeterminism versus determinism for two-way finite automata: generalizations of Sipser’s separation. In: Baeten, J.C.M., Lenstra, J.K., Parrow, J., Woeginger, G.J. (eds.) ICALP 2003. LNCS, vol. 2719, pp. 439–451. Springer, Heidelberg (2003)
Kapoutsis, C.: Small sweeping 2NFAs are not closed under complement. In: Bugliesi, M., Preneel, B., Sassone, V., Wegener, I. (eds.) ICALP 2006. LNCS, vol. 4051, pp. 144–156. Springer, Heidelberg (2006)
Kapoutsis, C.: Deterministic moles cannot solve liveness. Journal of Automata, Languages and Combinatorics 12(1-2), 215–235 (2007)
Kapoutsis, C.: Two-way automata versus logarithmic space. In: Proceedings of Computer Science in Russia, pp. 359–372 (2011)
Leung, H.: Tight lower bounds on the size of sweeping automata. Journal of Computer and System Sciences 63(3), 384–393 (2001)
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, May 1-3, pp. 275–286. ACM, San Diego (1978)
Seiferas, J.I.: Untitled manuscript, communicated to M. 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
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kapoutsis, C.A. (2011). Nondeterminism Is Essential in Small 2FAs with Few Reversals. In: Aceto, L., Henzinger, M., Sgall, J. (eds) Automata, Languages and Programming. ICALP 2011. Lecture Notes in Computer Science, vol 6756. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22012-8_15
Download citation
DOI: https://doi.org/10.1007/978-3-642-22012-8_15
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-22011-1
Online ISBN: 978-3-642-22012-8
eBook Packages: Computer ScienceComputer Science (R0)