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.
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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)
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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
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DOI: https://doi.org/10.1007/978-3-642-22012-8_18
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