Abstract
We show how to calculate the maximum number of edits per character needed to convert any string in one regular language to a string in another language. Our algorithm makes use of a local determinization procedure applicable to a subclass of distance automata. We then show how to calculate the same property when the editing needs to be done in streaming fashion, by a finite state transducer, using a reduction to mean-payoff games. We show that the optimal streaming editor can be produced in PTIME.
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
Benedikt, M., Puppis, G., Riveros, C.: Regular repair of specifications. In: LICS (2011)
Ehrenfeucht, A., Mycielski, J.: Positional strategies for mean payoff games. J. of Game Theory 8, 109–113 (1979)
Karmarkar, N.: A new polynomial-time algorithm for linear programming. In: STOC, pp. 302–311 (1984)
Konstantinidis, S.: Computing the edit distance of a regular language. Inf. and Comp. 205(9), 1307–1316 (2007)
Krob, D.: The equality problem for rational series with multiplicities in the tropical semiring is undecidable. In: Kuich, W. (ed.) ICALP 1992. LNCS, vol. 623, pp. 101–112. Springer, Heidelberg (1992)
Matouek, J., Gärtner, B.: Understanding and Using Linear Programming (2006)
Mohri, M.: Finite-state transducers in language and speech processing. J. of Comp. Ling. 23(2), 269–311 (1997)
Mohri, M.: Edit-distance of weighted automata: general definitions and algorithms. J. of Found. of Comp. Sc. 14(6), 957–982 (2003)
Simon, I.: Recognizable sets with multiplicities in the tropical semiring. In: Koubek, V., Janiga, L., Chytil, M.P. (eds.) MFCS 1988. LNCS, vol. 324, pp. 107–120. Springer, Heidelberg (1988)
Wagner, R.A.: Order-n correction for regular languages. CACM 17(5), 265–268 (1974)
Wagner, R.A., Fischer, M.J.: The string-to-string correction problem. JACM 21(1), 168–173 (1974)
Zwick, U., Paterson, M.: The complexity of mean payoff games on graphs. Theor. Comput. Sci. 158, 343–359 (1996)
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
Benedikt, M., Puppis, G., Riveros, C. (2011). The Cost of Traveling between Languages. 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_18
Download citation
DOI: https://doi.org/10.1007/978-3-642-22012-8_18
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)