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Iteration of rational transductions

Published online by Cambridge University Press:  15 April 2002

Alain Terlutte  and
David Simplot
Alain Terlutte
Affiliation:
UPRESA 8022 du CNRS, LIFL, Université de Lille I, bâtiment M3, Cité Scientifique, 59655 Villeneuve-d'Ascq Cedex, France; ([email protected])
David Simplot
Affiliation:
UPRESA 8022 du CNRS, LIFL, Université de Lille I, bâtiment M3, Cité Scientifique, 59655 Villeneuve-d'Ascq Cedex, France; ([email protected])
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Abstract

The purpose of this paper is to show connections between iterated length-preserving rational transductions and linear space computations. Hence, we study the smallest family of transductions containing length-preserving rational transductions and closed under union, composition and iteration. We give several characterizations of this class using restricted classes of length-preserving rational transductions, by showing the connections with "context-sensitive transductions" and transductions associated with recognizable picture languages.

Keywords

Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 34 , Issue 2 , March 2000 , pp. 99 - 129
Copyright
© EDP Sciences, 2000

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References

Avizienis, A., Signed-digit number representations for fast parallel arithmetic. IRE Trans. Electronic Computers 10 (1961) 389-400. CrossRef
J. Berstel, Transductions and Context-Free Languages. Teubner Studienbücher, Stuttgart (1979).
Clerbout, M. and Latteux, M., Partial commutations and faithful rational transductions. Theoret. Comput. Sci. 34 (1984) 241-254. CrossRef
S. Eilenberg, Automata, Languages and Machines, Vol. A. Academic Press, New York (1974).
Elgot, C.C. and Mezei, J.E., On relations defined by generalized finite automata. IBM J. Res. Develop. 9 (1965) 47-68. CrossRef
D. Giammarresi and A. Restivo, Two-dimensional languages, in Handbook of Formal Languages, edited by A. Salomaa and G. Rozenberg, Vol. 3. Springer-Verlag, Berlin (1997) 215-267.
Greibach, S.A., Full AFL's and nested iterated substitution. Inform. and Control (Shenyang) 16 (1970) 7-35. CrossRef
T. Harju and J. Karhumäki, Morphisms, in Handbook of Formal Languages, edited by A. Salomaa and G. Rozenberg, Vol. 1. Springer-Verlag, Berlin (1997) 439-510.
Immerman, N., Nondeterministic space is closed under complementation. SIAM J. Comput. 17 (1988) 935-938. CrossRef
Kuroda, S.-Y., Classes of languages and linear bounded automata. Inform. and Control (Shenyang) 7 (1964) 207-223. CrossRef
Latteux, M. and Simplot, D., Recognizable picture languages and domino tiling. Theoret. Comput. Sci. 178 (1997) 275-283. CrossRef
Latteux, M. and Simplot, D., Context-sensitive string languages and recognizable picture languages. Inform. and Comput. 138 (1997) 160-169. CrossRef
M. Latteux, D. Simplot and A. Terlutte, Iterated length-preserving rational transductions, in Proc. 23rd Symposium on Mathematical Foundations of Computer Science (MFCS'98) (Brno, Czech Republic, 1998), edited by L. Brim, J. Gruska and J. Zlatuska. Springer-Verlag, Berlin, Lecture Notes in Comput. Sci. 1450 (1998) 286-295.
Latteux, M. and Turakainen, P., On characterizations of recursively enumerable languages. Acta Inform. 28 (1990) 179-186. CrossRef
Leguy, J., Transductions rationnelles décroissantes. RAIRO Theoret. Informatics Appl. 15 (1981) 141-148. CrossRef
É. Lilin, Une généralisation des semi-commutations. Tech. Rep. it-210, L.I.F.L., Université Lille 1, France (1991).
Muller, J.-M., Some characterizations of functions computable in on-line arithmetic. IEEE Trans. Comput. 43 (1994) 752-755. CrossRef
Nivat, M., Transductions des langages de Chomsky. Ann. Inst. Fourier (Grenoble) 18 (1968) 339-456. CrossRef
Schützenberger, M.P., Sur les relations rationnelles entre monoïdes libres. Theoret. Comput. Sci. 3 (1976) 243-259. CrossRef
D. Simplot and A. Terlutte, Closure under union and composition of iterated rational transductions (in preparation).
Szelepcsényi, R., The method of forced enumeration for nondeterministic automata. Acta Inform. 26 (1988) 279-284. CrossRef
Szijártó, M., A classification and closure properties of languages for describing concurrent system behaviours. Fund. Inform. 4 (1981) 531-549.
P. Turakainen, Transducers and compositions of morphisms and inverse morphisms, in Studies in honour of Arto Kustaa Salomaa on the occasion of his fiftieth birthday. Ann. Univ. Turku. Ser. A I 186 (1984) 118-128.
Wood, D., Iterated a-NGSM maps and $\Gamma$ systems. Inform. and Control (Shenyang) 32 (1976) 1-26. CrossRef