Abstract
We present a class of infinite automata, in which all local computations are performed by finite state machines. These automata characterize an abstract family of languages which does not seem to coincide with any other known class, and which seems to cut across the Chomsky hierarchy. We show results regarding recognizing power and closure properties, and sketch the use of machine growth as a refined measure of complexity with respect to some well-known measures.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Demri, S., Finkel, A., Goranko, V., van Drimmelen, G.: Model-checking CTL * over flat Presburger counter systems. Journal of Applied Non-classical Logics 20, 313–343 (2010)
Frougny, C., Sakarovitch, J.: Synchronized rational relations of finite and infinite words. Theor. Comput. Sci. 108(1), 45–82 (1993)
Hawkins, J.A.: A Performance Theory of Order and Constituency. Cambridge Univ. Pr., Cambridge (1994)
Kaneps, J., Freivalds, R.: Minimal nontrivial space complexity of probabilistic one-way turing machines. In: Rovan, B. (ed.) MFCS 1990. LNCS, vol. 452, pp. 355–361. Springer, Heidelberg (1990)
Khoussainov, B., Nerode, A.: Automatic presentations of structures. In: Leivant, D. (ed.) LCC 1994. LNCS, vol. 960, pp. 367–392. Springer, Heidelberg (1995)
Kornai, A.: Natural languages and the chomsky hierarchy. In: Proceedings of the 2nd European Conference of the ACL 1985, pp. 1–7 (1985)
MacNaughton, R., Papert, S.: Counter-free Automata. M.I.T. Press, Cambridge (1971)
Marcus, M., Hindle, D., Fleck, M.: D-Theory: Talking about talking about trees. In: Proceedings of the 21st Annual Meeting of the ACL 1983, pp. 129–136 (1983)
Rubin, S.: Automata presenting structures: A survey of the finite string case. Bulletin of Symbolic Logic 14(2), 169–209 (2008)
Shallit, J., Breitbart, Y.: Automaticity: Properties of a measure of descriptional complexity. In: Enjalbert, P., Mayr, E.W., Wagner, K.W. (eds.) STACS 1994. LNCS, vol. 775, pp. 619–630. Springer, Heidelberg (1994)
Stabler, E.P.: The finite connectivity of linguistic structure. In: Clifton, C., Frazier, L., Rayner, K. (eds.) Perspectives on Sentence Processing, pp. 303–336. Lawrence Erlbaum, Mahwah (1994)
Trakhtenbrodt, B.A., Barzdin, Y.M.: Finite Automata. North Holland, Amsterdam (1973)
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
Wurm, C. (2011). Regular Growth Automata: Properties of a Class of Finitely Induced Infinite Machines. In: Kanazawa, M., Kornai, A., Kracht, M., Seki, H. (eds) The Mathematics of Language. MOL 2011. Lecture Notes in Computer Science(), vol 6878. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23211-4_12
Download citation
DOI: https://doi.org/10.1007/978-3-642-23211-4_12
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-23210-7
Online ISBN: 978-3-642-23211-4
eBook Packages: Computer ScienceComputer Science (R0)