Abstract
We introduce and investigate revolving-input finite automata, which are nondeterministic finite automata with the additional ability to shift the remaining part of the input. We consider three different modes of shifting, namely revolving to the left, revolving to the right, and circular interchanging. We show that the latter operation does not increase the computational power of finite automata, even if the number of revolving operations is unbounded. The same result is obtained for the former two operations in case of an arbitrary but constant number of applications allowed. An unbounded number of these operations leads to language families that are properly contained in the family of context-sensitive languages, are incomparable with the family of context-free languages, and are strictly more powerful than regular languages. Moreover, we show that right revolving can be simulated by left revolving, when considering the mirror image of the input.
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
Bordihn, H., Holzer, M., Kutrib, M.: Input reversals and iterated pushdown automata: A new characterization of khabbaz geometric hierarchy of languages. In: Calude, C.S., Calude, E., Dinneen, M.J. (eds.) DLT 2004. LNCS, vol. 3340, pp. 102–113. Springer, Heidelberg (2004)
Chomsky, N.: Formal Properties of Grammars. In: Handbook of Mathematic Psychology, vol. 2, pp. 323–418. Wiley & Sons, New York (1962)
Evey, R.J.: The Theory and Applications of Pushdown Store Machines. Ph.D thesis, Harvard University, Massachusetts (1963)
Ginsburg, S.: Algebraic and Automata-Theoretic Properties of Formal Languages. North-Holland, Amsterdam (1975)
Ginsburg, S., Greibach, S.A., Harrison, M.A.: One-way stack automata. Journal of the ACM 14, 389–418 (1967)
Ginsburg, S., Spanier, E.H.: Control sets on grammars. Mathematical Systems Theory 2, 159–177 (1968)
Greibach, S.A.: An infinite hierarchy of context-free languages. Journal of the ACM 16, 91–106 (1969)
Holzer, M., Kutrib, M.: Flip-pushdown automata: k +1 pushdown reversals are better than k. In: Baeten, J.C.M., Lenstra, J.K., Parrow, J., Woeginger, G.J. (eds.) ICALP 2003. LNCS, vol. 2719, pp. 490–501. Springer, Heidelberg (2003)
Khabbaz, N.A.: Control sets and linear grammars. Information and Control 25, 206–221 (1974)
Khabbaz, N.A.: A geometric hierarchy of languages. Journal of Computer and System Sciences 8, 142–157 (1974)
Sarkar, P.: Pushdown automaton with the ability to flip its stack. Report TR01-081, Electronic Colloquium on Computational Complexity, ECCC (2001)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Bordihn, H., Holzer, M., Kutrib, M. (2005). Revolving-Input Finite Automata. In: De Felice, C., Restivo, A. (eds) Developments in Language Theory. DLT 2005. Lecture Notes in Computer Science, vol 3572. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11505877_15
Download citation
DOI: https://doi.org/10.1007/11505877_15
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-26546-7
Online ISBN: 978-3-540-31682-4
eBook Packages: Computer ScienceComputer Science (R0)